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Chapter 9: Q 19. (page 565)

Making conclusions A student performs a test of H0:p=0.75versus Ha:p<0.75at α=0.05significance level and gets a P-value of 0.22

The student writes: “Because the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Short Answer

Expert verified

As Pvalue is large, we cannot rejectH0. Null hypothesis is not false.

Step by step solution

01

Given Information

It is given that P=0.22=22%

α=0.05

H0:p=0.75

H1:p<0.75

02

Explanation

If Pvalue<α, reject null hypothesis

Here it is not fulfilled as 0.22>0.05⇒Fail to rejectH0

The statement having issues are:
  • Never accepting H0
  • There is never convincing proof that null hypothesis is true, instead it can be that null hypothesis is not true.

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Most popular questions from this chapter

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is 0.975pound.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in part (a) is 0.0806. Interpret the P-value.

d. What conclusion would you make at the α=0.01 significance level?

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by

a. using only volunteers from the basketball team in the experiment.

b. usingα=0.05 instead of α=0.05

c. using α=0.05instead of α=0.01

d. giving the drug to 25 randomly selected students instead of 50.

e. using a two-sided test instead of a one-sided test.

Don’t argue Refer to Exercises 2 and 12.

a. What conclusion would you make at the α=0.01 level?

b. Would your conclusion from part (a) change if a 5% significance level was used

instead? Explain your reasoning.

Fire the coach!A college president says, “More than two-thirds of the alumni support my firing of Coach Boggs.” The president’s statement is based on 200emails he has received from alumni in the past three months. The college’s athletic director wants to perform a test of H0:p=2/3versus Ha:p>2/3, where p= the true proportion of the college’s alumni who favor firing the coach. Check if the conditions for performing the significance test are met.

Attitudes Refer to Exercise 4. In the study of older students’ attitudes, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101.

a. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.
See all solutions

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