Wahat are the null and alterative hypothesis?

Question

A large univesrity says the mean number of class room hours per week for full time falculty is more than 9. So the null & alterative hypothesis are?

Answer 1

You will be testing to see if a particular teacher, or set of teachers, has a statistically different number of hours per week.



The null hypothesis says that, no, there is not a difference between this group and the whole faculty. Any difference that may exist is small enough to be attributed to small random deviations from the maximum of 9.



The alternative hypothesis says that there is a difference between this group and the whole faculty, a difference that cannot be attributed to random deviations greater than 9.



You automatically assume the null hypothesis because no evidence is required to support it (hence "null" meaning no proof necessary). If your statistical tests show otherwise, you reject the null hypothesis and accept the alternative. This can be determined by a number of statistical tests. In this case, you'd probably use a z-test.

Answer 2

Let μ be the number of hours full time faculty spend in the class room per week.



the hypothesis test will depend on what you want to do. Do you want to set up the hypothesis test to support the claim? if so then you have:



H0: μ ≤ 9 vs H1: μ > 9



if you want to refute the claim then the hypothesis test is:



H0: μ ≥ 9 vs. H1: μ < 9



if you just want to show that the value of 9 is not correct you have:



H0: μ = 9 vs. H1: μ ≠ 9









Consider the hypothesis as a trial against the null hypothesis. the data is evidence against the mean. you assume the mean is true and try to prove that it is not true. After finding the test statistic and p-value, if the p-value is less than or equal to the significance level of the test we reject the null and conclude the alternate hypothesis is true. If the p-value is greater than the significance level then we fail to reject the null hypothesis and conclude it is plausible. Note that we cannot conclude the null hypothesis is true, just that it is plausible.



If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be μ = d vs the alternate hypothesis μ ≠ d



if the question ask to test for an inequality you make sure that your results will be worth while. for example. say you have a steel bar that will be used in a construction project. if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.



if the null was μ ≥ 100,000 vs the alternate μ < 100,000 then will will have a meaningless test. in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar. However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000. You cannot ever conclude that the null is true. as a result you should not use the bar because you do not have proof that the mean strength is high enough.



if the null was μ ≤ 100,000 vs. the alternate μ > 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it. in this case you have a meaningful result.



Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.

Answer 3

the null hypothesis, Ho, mean hours <= 9

the alternative hypothesis, Ha, mean hours > 9

Your analysis/calculation will either accept or reject the null hypothesis. Rejecting the null hypothesis does not prove it, it just means there was not enough evidence to prove the alternative.

Answer 4

the null H0: µ0=9

Alternative

Ha: µ>9

you reject the null if (z or t)>(zα or tα)

depending on the number of students