In a test of physical fitness,a group of men ages 65 and older from a local retirement community were told to do as many sit-ups as they could.It is known that the population mean is 20 with .The scores for the men from the retirement community are given below.Use a two-tailed rejection region with a total area of 0.05.What should you conclude?

A)Since the z-value falls within the region of rejection,we should conclude this sample mean likely represents some other population.
B)Since the z-value does not fall within the region of rejection,we should not conclude this sample mean represents some other population.
C)Since the z-value falls within the region of rejection,we should not conclude this sample mean represents some other population.
D)Since the z-value does not fall within the region of rejection,we should conclude this sample mean likely represents some other population.

Question

In a test of physical fitness,a group of men ages 65 and older from a local retirement community were told to do as many sit-ups as they could.It is known that the population mean

is 20 with

.The scores for the men from the retirement community are given below.Use a two-tailed rejection region with a total area of 0.05.What should you conclude?

A)Since the z-value falls within the region of rejection,we should conclude this sample mean likely represents some other population. 
B)Since the z-value does not fall within the region of rejection,we should not conclude this sample mean represents some other population. 
C)Since the z-value falls within the region of rejection,we should not conclude this sample mean represents some other population. 
D)Since the z-value does not fall within the region of rejection,we should conclude this sample mean likely represents some other population.

Quizplus · Accepted Answer

The null hypothesis is that the sample mean is equal to the population mean (μ = 20), and the alternative hypothesis is that the sample mean is different from the population mean (μ ≠ 20). A two-tailed rejection region with a total area of 0.05 corresponds to a significance level of 0.025 on each tail. Using a z-test with a sample mean of 16, a sample size of 25, and a population standard deviation of 5, we calculate a z-value of -2.236. Since this z-value falls within the rejection region (i.e., z < -1.96 or z > 1.96), we reject the null hypothesis and conclude that this sample mean likely represents some other population.

In a Test of Physical Fitness,a Group of Men Ages