Question

A simple random sample generated 12 male and 18 female adults identified by their primary care physicians as being over-weight. These adults were fed a special high protein diet for a month and had a sample mean weight loss of 10 pounds with a sample standard deviation of 3.2 pounds. We would like to conduct a test to determine whether the average weight loss for all adults is less than 11 pounds at a 1% level of significance.

What would be the appropriate test statistic?

Select one:

a. matched paired test

b. confidence interval using t      

c. confidence interval using z

d. one-sample t-test   

e. one-sample z-test

Answer 1

A simple random sample generated 12 male and 18 female adults identified by their primary care physicians as being over-weight. These adults were fed a special high protein diet for a month and had a sample mean weight loss of 10 pounds with a sample standard deviation of 3.2 pounds. We would like to conduct a test to determine whether the average weight loss for all adults is less than 11 pounds at a 1% level of significance.

If you collect two measurements on same adults or same students or same car then each pair of observations is closely related. For example marks of student before reading reference book and after reading reference book This produces a set of paired observations for each adults. In this case our appropriate test statistic matched paired test. By matched paired test we mainly test is there significance difference present or not for dependent sample. But for our problem hypothesized mean difference is not given. So matched paired test is not appropriate.

[ For matched paired test null and alternative hypothesis is given by,

vs [ Here is not given ] ]

One-sample-t (when sample sd is not known) and One-sample-Z (when sample sd is known) test is mainly used to test the statistical difference between a sample mean and a hypothesized mean of population. So this two test also not appropriate for our situation because here our data set is paired.

Confidence intervals gave us an upper limit and lower limit for population mean or population mean difference. And here we perform a test for weight loss.So confidence interval gave us an idea of a lower limit and upper limit of weight loss for all adults and After getting upper limit of weight loss we take decision about weight loss for all adults is less than 11 pounds or not at 1% level of significance. So for this situation Confidence intervals test is appropriate.

But here population standard deviation is not given so we can't perform confidence interval using z .

So our appropriate test statistic is confidence interval using t.   

Answer:- Correct answer is " Option b. confidence interval using t "