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Chapter 8: Q23BSC (page 356)

Critical Values. In Exercises 21鈥�24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of \(\alpha \)= 0.05, should we reject \({H_0}\)or should we fail to reject \({H_0}\)?

Exercise 19

Short Answer

Expert verified

a.The critical values are -1.96 and 1.96.

b.The null hypothesis is rejected.

Step by step solution

01

Given information

A test statistic value of \(z = 2.01\) is obtained, and the claim to be tested is \(p \ne 0.345\).

02

Hypotheses and tail of the test

In correspondence with the given claim, the following hypotheses are set up:

Null Hypothesis:\(p = 0.345\)

Alternative Hypothesis:\(p \ne 0.345\)

Since there is a not equal sign in the alternative hypothesis, the test is two-tailed.

03

Critical value

a.

The critical values of z corresponding to the two-tailed test at \(\alpha = 0.05\)are -1.96 and 1.96.

04

Decision about the test

b.

If the test statistic value does not lie between the critical values, then the null hypothesis is rejected.

Here, the value of the test statistic (2.01) does not lie between the critical values (greater than 1.96). Thus, the null hypothesis is rejected.

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Most popular questions from this chapter

In Exercises 9鈥�12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

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Technology. In Exercises 9鈥�12, test the given claim by using the display provided from technology. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

Tornadoes Data Set 22 鈥淭ornadoes鈥� in Appendix B includes data from 500 random tornadoes. The accompanying StatCrunch display results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.5 miles.

Critical Values. In Exercises 21鈥�24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

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Exercise 19

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