Question

8.1 What is the purpose of hypothesis testing?

8.2 Coach McWilliams, a P.E. teacher wants to increase the number of sit-ups her students can do in one minute. Throughout the quarter, McWilliams requires her class to do an extra 2-minute plank each day. Assuming that the population (national) mean for sit-ups in a minute is 30 (σ = 12) and sit-up scores are normally distributed, what would be the null-hypothesis for McWilliams’ plan?

8.3 What is McWilliams’ alternative-hypothesis?

8.4 At the beginning of the year, Coach McWilliams’ 20 students do an average of 26 sit-ups in one minute. Are her students’ times “expected” (that is, not reliably different from the population mean) if we are using an alpha level of .05 for our decision-making criteria? SHOW WORK

8.5 At the end of the quarter after completing the training program, Coach McWilliams’ 20 do an average of 38 sit-ups in one minute. Using an α = .05, what decision will you make as a result of the hypothesis test?

Answer 1

8.1:

The purpose of hypothesis test is to make inference about the population on the basis of sample evidence taken from population under study.

8.2

The null hypothesis is:

8.3:

The alternative hypothesis is:

8.4:

Here we have

Here we need to test whether her students’ times are as “expected”so in this case altermative hypothesis is:

Test is two tailed. The test statistics is

The p-value is:

p-value = 2P(z < -1.49) = 0.1362

Since p-value is greater than 0.05 so we fail to reject the null hypothesis. That is we can conclude that her students’ times are as “expected”.

8.5:

Here we have

Test is right tailed. The test statistics is

The p-value is:

p-value = 1 - P(z < 2.98) = 0.0014

Since p-value is greater than 0.05 so we reject the null hypothesis. That is we can conclude that  the training program is effective in increasing the number of sit-ups.