from three days regularly i was trying to touch the concept of testing hypothesis but your class gave me wonderful overall summerized concept, thank u sir
Welcome... Keep watching keep learning... There are playlists on various topics on my channel so don't forget to visit and subscribe... Also don't forget to recommend my lectures and my channel to others, as only you people are my brand ambassadors... There will be more new lectures soon... :)
Welcome! Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
Respected Prashant Sir Thankyou so much for the videos. Let me share you a small story . I m an MBA student currently in 3rd semester. when I was in 2nd semester ,I was having a subject called Business Research Methodology. When I appeared in Mid semester examination i score 27 out of 100 (lowest in class) then I got your tutorial videos on RUclips.. and in end semester examination I scored 81(Highest in the class) thankyou for your guidance.. lots of respect. regards Kartik Singh
after repeated learning elsewhere only aftewr hearing your lecture i coul d understand p value alpha and their relation , thank yu very much sir . Most clear cut and emphatic and straight forward explanation and teaching . h
Welcome! Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
No, we can't determine/write the Null and Alternative Hypothesis vice versa. Just remember that Null Hypothesis is always about "No Difference". e.g. (i) there is no significant difference between population mean and sample mean (in case of test of significance of single mean); (ii) there is no significant difference between two sample means (in case of the test of significance of difference between two means); (iii) there is no significant difference between the two proportions (in case of the test of significance of difference between two proportions.... And the alternative hypothesis is written as "there is significant difference between...." Of course, we should always write the wordings of the null and alternative hypothesis according to the subject matter of the problem/case, keeping these things into our mind. Please never make a mistake of expecting that anyone can understand how to determine/write the Null and Alternative Hypothesis just by learning one or two cases. We need to learn different types of Null and Alternative Hypothesis with the help of variety of examples. The tragedy is, nowadays most of the teachers and authors write the hypothesis using the signs of the parameters only. So, it becomes too much difficult for the students/learners to understand the hypothesis while studying from the solved problems. We should always write the hypothesis both in words and in signs, because at the end we should be clear about the conclusion with reference to the subject matter of the problem... :)
what about if sample is less than 30 and also sample standrd deviation given which test will be applied t or z my sir said in such case we would use z test but i confused pls clarify it
Test of significance means the test of significance of the existing population statistic or existing theory or belief... something like we challenge the existing statistic/theory/belief and try to test/check whether it still stands worth or it should be substituted by the new statistic/theory after arriving at the conclusion of our test... :)
There are two types of tables available - (i) covering the whole area under the curve, i.e. LHS and RHS; (ii) covering the area between mid-point, x = mean, i.e. z = 0, and the calculated value of 'z'. You have found the value from the first type of table, which is nowadays given in almost all the reference books, but to be very frank students and sometimes teachers too face problems while using it to solve the ND and Z-test problems. According to the situation, we need to subtract that area from 1 or 0.5 from that area while we use the first type of table. In this-value' = 1 - 0.9675 We, here, are habituated to use the second type of table from which we directly get the area between z=0 and z= calculated value. So, in this lecture I have shown 'p-value' = 0.5 - area.
Due to some past experiences, I can't share my email address here. The flow keeps me busy only in solving personal queries and that ultimately prevents me from the creative work relevant to the new video lectures... I hope you can understand my situation. Of course, I frequently check here and my FB page for comments and queries from the students... :)
sir pls give the solution for the following problem in z test: The quality control department of a food processing firm specifies that the mean net weight per package of a certain food must be 20 gm. Experience has shown that the weights are approximately distributed with a standard deviation of 15 gm. If a random sample of 15 packages yields a mean weight of 19.5 gram, is this sufficient evidence to indicate that the true mean weight of the package has decreased.
This is a case of "t-test". To be precise, it's a case of one tailed test. The Ho will be "There is no significant change in the mean weight of the packages" (μ = 20) and the Ha or H1 should be "The mean weight of the packages has DECREASED significantly" (μ
sir, pls give the sollution for the following problem in z test: a manufacturer of steels rods considers that the manufacturing is working properly, if the mean length of the rods is 8.6 inches. The standard deviation of these rods about 0.3 inch. The manufacturer would like to see, if the process is working correctly by taking a random sample of size n = 36. There is no indication whether or not the rods may be too short or long. ? sir pls solve my problem
μ = 8.6, σ = 0.3, n = 36. So, it is a case with large sample. As there is no clear information, take the level of significance of 5%, hence, α = .005. Take this as a two-tailed case. The critical value of Z for two-tailed test at 5% level of significance is ±1.96. Now substitute all these values in the formula Z = (x̅ - μ) / (σ/√n) and then simplify it to find the range of value of x̅ (upper limit and lower limit of the values of x̅), i.e. range of sample mean of the length of rods manufactured when rods may not be too short or long....
sir i am from nepal and student of mbs(m.com) .in our course author are using population aaproach the if i follow sample approach the can i get marks or it became wrong.
There is no difference in the method of calculation and arriving at conclusion. The only thing which can be different is kind of data given in the problem. Most of the problems are solved in the same way under both the assumptions, but few might be different if prepared deliberately considering the population approach. So, you need not worry too much about this thing. Be alert only where the sample is small and population variance/SD is available because in such a situation it will be advisable for you to use population approach...:)
Thank you sir for make it understandable.. sir i have one question my research study on effectiveness of structured teaching programme. so in pre test mean is calculated 11.24 SD 4.09 and in post test mean 28.12 and SD 2.6. I used z test for significance but I have no value of population mean. and z test calculated value got 31.84. so now my question is.. is it correct or what? sir please solve my problem.
If you want to study "effectiveness" of something, you should use "The Paired t-Test" (yes, t-Test, I am not mistaking. We may use t-Test even if the sample size is greater than 29). The reason is, in this kind of research analysis we actually deal with a single or same sample twice - before and after implementing the teacher programme. For this purpose you have to consider "degrees of freedom = n - 1" (yes, not n1 + n2 - 2 because you are not dealing with 2 different samples, you are dealing with the same sample at two different points of time before and after implementing teaching programme) and you have to take the critical value of 't' for the purpose of comparison and to arrive at the conclusion about the effectiveness of the teaching programme. If the calculated value of 't' is greater than the critical value, you may conclude that the structured teaching programming is effective presuming 'd = score after minus score before...'. The critical value of 't' for up to 100 degrees of freedom are available in the table of t, which is freely/easily available online. (Critical values of Z are also available from the same table at infinite degrees of freedom...) Before performing this Paired t-Test for your data, it will be better you study and learn that test from my video lectures. For this purpose you just need to go to my channel and there is a separate playlist on t-Test which includes the video(s) on Paired t-TEST... :)
We have to decide this case-to-case separately. There are playlists on various tests like Z, t, Chi-square and F and I have discussed everything in detail while discussing the solutions of various different types of cases/problems...
Level of significance and "one tailed or two tailed' test both are different things... It's too long to answer/discuss here... I am working on the same topic and from the coming week I am going to upload more videos on lectures on tests of hypothesis... :)
Where the questions are of small size, I have written on the board itself and in all other cases the questions and other important notes have been written as note under the video you are watching. To read that content you need to press the 'Show more' button which you can see under the video every time.
Sir why are u saying that if n= greater than 100 then we must sure that we have to use z test while indian author say if n= 30 or greater than 30 we should use z test ?? Plz answer ?
Yes, n>=30 is considered a large sample. But, in real life when we want to test the hypothesis about mean(s) for some certain degrees of freedom and not at the infinite degrees of freedom (as in the case of Z-test) we have to select the sample accordingly and in such a case we have to use t-test, instead of Z-test, even if the sample size n.=30. OR Just imagine a case like "Paired t-test". It is not at all compulsory to take a small sample only. According to the size of the population we even need to take a sample of size 30 or more and analyse it twice, before and after some specific act or action or decision. In such a case we need to perform "Paired t-test" for a large sample.
Prashant Puaar sir thanks for your reply. As i don't know about paired t test so i m not clear...did you mean 't-test for double mean' as 'paired t-test ?'
No, 't-test of significance of difference between two means' and 'Paired t-test' both are not the same tests. Both are totally different. In case of the 't-test of significance of difference between two means' there must be two different samples randomly selected from the two different populations, while in case of the 'Paired t-test' there will be only one sample randomly selected from only one population but the sample is analysed twice at two different points of time before and after some specific process/event/decision/change, in studying the effect of which the researcher is interested...
It can be Z-test only if we use parameters like mean and SD. If you have used ranks (I don't know about the type of data on which you are working), no mean or SD is possible and, hence, it can't be Z-test...
intelligence test on two group one group having 121girls and other group 81 boys gives the following result group of girl mean 84 standard devation 10 group of boys mean 81 standard deviation 12 examine the diff between sample mean is significant given z=1.96 which formula apply in this case plz request to everyone plz tell me
No, this should not be solved as a case of 'one-tailed test' because we just need to check 'whether the sample belongs to a population having specific parameters'. We should treat it a case' of one-tailed teat ONLY IF we need to check that the mean takes value 'greater than' or 'less than ' a specific value. The sample may belong to a population even if its mean is greater than the population mean or less than that up to a certain extent, i.e. for a sample to belong to a particular population it is not at all necessary that its sample mean to be exactly greater than or less than the population mean ... A sample which has a mean less than the population mean may belong to that population and in the same way a sample having a mean greater than the population mean may also belong to the population, of course, it depends on the confidence interval... Always read carefully the statement telling us what do we need to test, as it always gives indications about the type of test, one-tailed or two-tailed... :)
Ek no
Best lecture for hypothesis Testing.
Clear point to point discussion .
Thank you sir for sharing with us.
very convincing. simplest and the best way of presentation
sir your teaching is awesome. cleared within 30 min which i have been struggling over hours
from three days regularly i was trying to touch the concept of testing hypothesis but your class gave me wonderful overall summerized concept, thank u sir
Welcome... Keep watching keep learning... There are playlists on various topics on my channel so don't forget to visit and subscribe... Also don't forget to recommend my lectures and my channel to others, as only you people are my brand ambassadors... There will be more new lectures soon... :)
Excellent explanation sir. GOD bless you with all necessary strength to pass this legacy to younger generation.
Amazing sir your class to listen 👍👍👍👍👍
Keep watching
Thank you thank you sir..........ur teaching style Is awesome
Its a nice video lecture for Testing of hypothesis,Thank you sir.
wow....... amazing explanation for such type of topic. really like
Thanks a ton sir!!! You are the best teacher in the world! It really explained me very well!!
Thank you so much, I can understand better sir.. please continue teaching
Thankyou so much sir for this video.never before understand the concept of testing of hypothesis ;you did it so well.👍🏾👍🏾😊
I just loved your session sir.........
thank you very much..............
again thanx sir..
again thanx....
Thank you so much sir...clear explanations u have given.. Very helpful ..
Great teaching, sir 👏👏👏 🙇
Thnku very much... Really helpful and understood everything 🙌🙌
Respected Sir, the methodology adopted by you is more impressive and understandable.
I understand very much better than my college clasess
nice lecture and yes sample size approach is better than the s.d approach
ohh yess, finally i found my teacher 🤎
Welcome! Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
No words to say for your explanation sir
thank u sir....helped me alot for semester...Nice explanation
wow I wonder how come i understood this concept in 30 minutes, whereas I didnt understand anything by attending 50 minutes lecture. thank you sir
thank you sir
Awesome explanation & teaching😍😍😎
india is full of gems
Thank you so much. Beautiful explanation!!
thank you so much, sir. it's very useful for me.
Thanks sir My doubt was cleared.
Amazing lecture sir. Thanks alot!! It helped alot! ♥️♥️
You are great sir .... i want to make myself like you.....
Stupendous explanation sir. keep it up.
superb voice sir, i like u teaching style and if our professor is having such a wonderful voice.It would not be possible for me to sleep in his class
Respect sire...best lecture i have ever seen in youtube about hypothesis...Thanks a lot ❤
Thank you very much for appreciating with such nice words... :)
But sir i have another question why we should see the 't' table value when we are doing Z test?
Respected Prashant Sir
Thankyou so much for the videos.
Let me share you a small story .
I m an MBA student currently in 3rd semester.
when I was in 2nd semester ,I was having a subject called Business Research Methodology.
When I appeared in Mid semester examination i score 27 out of 100 (lowest in class) then I got your tutorial videos on RUclips..
and in end semester examination I scored 81(Highest in the class)
thankyou for your guidance..
lots of respect.
regards
Kartik Singh
That's really very good. Keep it up. Best of Luck... :)
Sir, you teach in a lucid manner and it makes things easier. Thank You:)
Simply Brilliant!
Thank u sir from bottom of my heart
Thank you sir may Allah bless you
Best experince
after repeated learning elsewhere only aftewr hearing your lecture i coul d understand p value alpha and their relation , thank yu very much sir . Most clear cut and emphatic and straight forward explanation and teaching . h
Well elaborated sir ji
Thank you sir❤️❤️🇳🇵
Welcome! Keep watching keep learning... Visit and subscribe my channel and don't forget to recommend my channel and lectures/playlists to others also... you will find so many subjects/topics... Thanks... :)
Thanks,,
How do we find out the z test is one tailed or two tailed?
Thanku sir . Please upload videos of non parametric tests
very good for good concept
Thank you, Harish Kumar... :)
What if we get z value a greater one like 30, 250.... If that's the case we cannot find it in the normal distribution table.. Right?
Sir which test to use for checking homogeneous correlation coefficient on small samples(n
amazing explanation :)
Well done young man
Thank you so much sir!!!
I should understand it sir
nice video sir !!
Nice teaching
thanks sir
from the quetion how to frame null hypothesis and alternative hypothesis.... we can even do vice versa of the null and alternative hypothesis
No, we can't determine/write the Null and Alternative Hypothesis vice versa. Just remember that Null Hypothesis is always about "No Difference". e.g. (i) there is no significant difference between population mean and sample mean (in case of test of significance of single mean); (ii) there is no significant difference between two sample means (in case of the test of significance of difference between two means); (iii) there is no significant difference between the two proportions (in case of the test of significance of difference between two proportions.... And the alternative hypothesis is written as "there is significant difference between...."
Of course, we should always write the wordings of the null and alternative hypothesis according to the subject matter of the problem/case, keeping these things into our mind. Please never make a mistake of expecting that anyone can understand how to determine/write the Null and Alternative Hypothesis just by learning one or two cases. We need to learn different types of Null and Alternative Hypothesis with the help of variety of examples.
The tragedy is, nowadays most of the teachers and authors write the hypothesis using the signs of the parameters only. So, it becomes too much difficult for the students/learners to understand the hypothesis while studying from the solved problems. We should always write the hypothesis both in words and in signs, because at the end we should be clear about the conclusion with reference to the subject matter of the problem... :)
Prashant Puaar thankyou so much sir
Thank you tonnes! Helped me alot!!
How do we find out two means i.e.,x bar n mu...
thanks sir ...love u
best lecture....ever seen
😍😍thhxuuuu soo much sir
Sir is there any video of theory of hypothesis where you are explaining meaning of sampling theory?
Wow... what an explanation...
Please make a vedio on sufficiency or sufficient estimator.
Thank you so much sir
Thank u so much sir
do you do online coaching sir
thank u sir thank u
Nice
How to get the area between z=0 to z=1.778, which table contains this information.?
what about if sample is less than 30 and also sample standrd deviation given which test will be applied t or z
my sir said in such case we would use z test but i confused
pls clarify it
n
+Prashant Puaar thanku sir for ur valuable advise
sir what is mean by test of significant?
Test of significance means the test of significance of the existing population statistic or existing theory or belief... something like we challenge the existing statistic/theory/belief and try to test/check whether it still stands worth or it should be substituted by the new statistic/theory after arriving at the conclusion of our test... :)
@@PUAARAcademy thank you sooooo much sir ^_^
Welcome... Keep watching keep learning... Don't forget to recommend my channel to others also...
Tq but how we we'll get critical values
tnqqq sir
sir , can u please tell me how you got the area of Z =1.78 is 0.4619 from Z table?
It's readily available from the table of "Area under Normal Curve", easily available online and in the form of booklet as well...:)
for 1.78 the value is 0.9625 and for -1.78 the value is 0.0375.If u want I can send from which Z table I am taking .please send ur gmail ID.
There are two types of tables available - (i) covering the whole area under the curve, i.e. LHS and RHS; (ii) covering the area between mid-point, x = mean, i.e. z = 0, and the calculated value of 'z'. You have found the value from the first type of table, which is nowadays given in almost all the reference books, but to be very frank students and sometimes teachers too face problems while using it to solve the ND and Z-test problems. According to the situation, we need to subtract that area from 1 or 0.5 from that area while we use the first type of table.
In this-value' = 1 - 0.9675
We, here, are habituated to use the second type of table from which we directly get the area between z=0 and z= calculated value. So, in this lecture I have shown 'p-value' = 0.5 - area.
Due to some past experiences, I can't share my email address here. The flow keeps me busy only in solving personal queries and that ultimately prevents me from the creative work relevant to the new video lectures... I hope you can understand my situation. Of course, I frequently check here and my FB page for comments and queries from the students... :)
Sir am not getting area value how to find
sir pls give the solution for the following problem in z test: The quality control department of a food processing firm specifies that the mean net weight per package of a certain food must be 20 gm. Experience has shown that the weights are approximately distributed with a standard deviation of 15 gm. If a random sample of 15 packages yields a mean weight of 19.5 gram, is this sufficient evidence to indicate that the true mean weight of the package has decreased.
This is a case of "t-test". To be precise, it's a case of one tailed test. The Ho will be "There is no significant change in the mean weight of the packages" (μ = 20) and the Ha or H1 should be "The mean weight of the packages has DECREASED significantly" (μ
Sir, is there any case where we use (x - u)/(sigma) alone instead of ( x - u)/(sigma/sqrt (n)).. Please reply sir 🙇
I know I'm late... But your teaching is very nice sir!
sir, pls give the sollution for the following problem in z test: a manufacturer of steels rods considers that the manufacturing is working properly, if the mean length of the rods is 8.6 inches. The standard deviation of these rods about 0.3 inch. The manufacturer would like to see, if the process is working correctly by taking a random sample of size n = 36. There is no indication whether or not the rods may be too short or long. ? sir pls solve my problem
μ = 8.6, σ = 0.3, n = 36. So, it is a case with large sample. As there is no clear information, take the level of significance of 5%, hence, α = .005. Take this as a two-tailed case. The critical value of Z for two-tailed test at 5% level of significance is ±1.96. Now substitute all these values in the formula Z = (x̅ - μ) / (σ/√n) and then simplify it to find the range of value of x̅ (upper limit and lower limit of the values of x̅), i.e. range of sample mean of the length of rods manufactured when rods may not be too short or long....
thank you sir
It is very useful for me
sir i am from nepal and student of mbs(m.com) .in our course author are using population aaproach the if i follow sample approach the can i get marks or it became wrong.
There is no difference in the method of calculation and arriving at conclusion. The only thing which can be different is kind of data given in the problem. Most of the problems are solved in the same way under both the assumptions, but few might be different if prepared deliberately considering the population approach. So, you need not worry too much about this thing. Be alert only where the sample is small and population variance/SD is available because in such a situation it will be advisable for you to use population approach...:)
Thank you sir for make it understandable.. sir i have one question my research study on effectiveness of structured teaching programme. so in pre test mean is calculated 11.24 SD 4.09 and in post test mean 28.12 and SD 2.6. I used z test for significance but I have no value of population mean. and z test calculated value got 31.84. so now my question is.. is it correct or what? sir please solve my problem.
sample size is 50
sample mean got 16.88
SD 3.77
SE 0.53
this formula used z= X bar/ SE
is it correct?
If you want to study "effectiveness" of something, you should use "The Paired t-Test" (yes, t-Test, I am not mistaking. We may use t-Test even if the sample size is greater than 29). The reason is, in this kind of research analysis we actually deal with a single or same sample twice - before and after implementing the teacher programme.
For this purpose you have to consider "degrees of freedom = n - 1" (yes, not n1 + n2 - 2 because you are not dealing with 2 different samples, you are dealing with the same sample at two different points of time before and after implementing teaching programme) and you have to take the critical value of 't' for the purpose of comparison and to arrive at the conclusion about the effectiveness of the teaching programme. If the calculated value of 't' is greater than the critical value, you may conclude that the structured teaching programming is effective presuming 'd = score after minus score before...'. The critical value of 't' for up to 100 degrees of freedom are available in the table of t, which is freely/easily available online. (Critical values of Z are also available from the same table at infinite degrees of freedom...)
Before performing this Paired t-Test for your data, it will be better you study and learn that test from my video lectures. For this purpose you just need to go to my channel and there is a separate playlist on t-Test which includes the video(s) on Paired t-TEST... :)
Thank you so much sir for your valuable suggestion. I have used paired t test and got t value 32.
Thank you sir again.
Can do it in 2days
nice nice
Thank you... :)
sir how to know the the one tail or two tail
We have to decide this case-to-case separately. There are playlists on various tests like Z, t, Chi-square and F and I have discussed everything in detail while discussing the solutions of various different types of cases/problems...
Plz.add video of t test
There are already and new are coming...
A coin was tossed 400 times and head turned up 216 times. Test the hypothesis that the coin is unbiased at 5 % level of significance..
sir, in Tamil 2nd year text book , it mentions that large sample means n>30, is it right?.
Pople Pandari n >= 30 is considered as large sample. So, n < 30 is small sample. 😊
thank you Sir
sir one more question is that , level of significance , how shall we decide?. (I.e. two tail or one tail)
Level of significance and "one tailed or two tailed' test both are different things... It's too long to answer/discuss here... I am working on the same topic and from the coming week I am going to upload more videos on lectures on tests of hypothesis... :)
hello sir we need question
jo aap padhate ho vo question ki pdf send kar skte ho
Where the questions are of small size, I have written on the board itself and in all other cases the questions and other important notes have been written as note under the video you are watching. To read that content you need to press the 'Show more' button which you can see under the video every time.
Sir why are u saying that if n= greater than 100 then we must sure that we have to use z test while indian author say if n= 30 or greater than 30 we should use z test ?? Plz answer ?
Yes, n>=30 is considered a large sample. But, in real life when we want to test the hypothesis about mean(s) for some certain degrees of freedom and not at the infinite degrees of freedom (as in the case of Z-test) we have to select the sample accordingly and in such a case we have to use t-test, instead of Z-test, even if the sample size n.=30.
OR Just imagine a case like "Paired t-test". It is not at all compulsory to take a small sample only. According to the size of the population we even need to take a sample of size 30 or more and analyse it twice, before and after some specific act or action or decision. In such a case we need to perform "Paired t-test" for a large sample.
Prashant Puaar sir thanks for your reply. As i don't know about paired t test so i m not clear...did you mean 't-test for double mean' as 'paired t-test ?'
No, 't-test of significance of difference between two means' and 'Paired t-test' both are not the same tests. Both are totally different.
In case of the 't-test of significance of difference between two means' there must be two different samples randomly selected from the two different populations, while in case of the 'Paired t-test' there will be only one sample randomly selected from only one population but the sample is analysed twice at two different points of time before and after some specific process/event/decision/change, in studying the effect of which the researcher is interested...
Thanks ❤
Sir, tame gujju cho ne?
Yes, proudly...:)
Thank you sir ... very helpful video.. but i want to ask one thing that is wilcoxon test is another name of z test??
No, it's not like that. Wilcoxon is a different test. Z-test is a parametric test, which this one is a non-parametric test...
Actually sir i m conducting a researsh study and my statistician done my analysis with z test by giving ranks ... is this possible?
It can be Z-test only if we use parameters like mean and SD. If you have used ranks (I don't know about the type of data on which you are working), no mean or SD is possible and, hence, it can't be Z-test...
present Einstein
Sir Your voice is not clear ...
Respected sir , Z critical 1.960 value kaise aayi
From table,z test table
intelligence test on two group one group having 121girls and other group 81 boys gives the following result
group of girl mean 84 standard devation 10
group of boys mean 81 standard deviation 12
examine the diff between sample mean is significant given z=1.96
which formula apply in this case
plz request to everyone plz tell me
Please go to the playlist of 'Z-Test' and watch the video on "Z-test for difference between two means" carefully... :)
Prashant Puaar
sir maine z test ka two different mean wala formula use kia tha
ya formula thik ha kya
Where is z test for two means
There is whole playlist on this topic and playlists on many other chapters/topics on my channel...:)
it is one tailed
No, this should not be solved as a case of 'one-tailed test' because we just need to check 'whether the sample belongs to a population having specific parameters'. We should treat it a case' of one-tailed teat ONLY IF we need to check that the mean takes value 'greater than' or 'less than ' a specific value. The sample may belong to a population even if its mean is greater than the population mean or less than that up to a certain extent, i.e. for a sample to belong to a particular population it is not at all necessary that its sample mean to be exactly greater than or less than the population mean ... A sample which has a mean less than the population mean may belong to that population and in the same way a sample having a mean greater than the population mean may also belong to the population, of course, it depends on the confidence interval... Always read carefully the statement telling us what do we need to test, as it always gives indications about the type of test, one-tailed or two-tailed... :)
Thank u sir... it helped me lot....😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘..................∞∞∞∞∞∞∞
pls ans me sir