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Chapter 8: Q6CQQ (page 356)

Conclusions True or false: The conclusion of “fail to reject the null hypothesis” has exactly the same meaning as “accept the null hypothesis.”

Short Answer

Expert verified

It is false that the meaning of “fail to reject the null hypothesis” is the same as “accept the null hypothesis”.

Step by step solution

01

Given information

The following statement is considered:

The conclusion of “fail to reject the null hypothesis” has exactly the same meaning as “accept the null hypothesis.”

02

Decision about the null hypothesis

It is a convention that if the p-value is greater than the significance level, the null hypothesis has failed to be rejected and is not accepted/supported.

In hypothesis testing, the null hypothesis can be considered as a negative result of a test.

The null hypothesis is constructed to be proved wrong.

It will be incorrect to conclude that you proved a negative result.

It will be wise to say that you did not have enough evidence to prove a positive result.

Accepting the null hypothesis means proving the negative result of the hypothesis test.

Failing to reject the null hypothesis means that there isn’t sufficient evidence to reject it for now.

Therefore, both phrases have different meanings. Thus, the given statement is false.

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Most popular questions from this chapter

In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

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a. Is the test two-tailed, left-tailed, or right-tailed?

b. What is the test statistic?

c. What is the P-value?

d. What is the null hypothesis, and what do you conclude about it?

e. What is the final conclusion?

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Exercise 17

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