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Chapter 8: Q22BSC (page 356)

Critical Values. In Exercises 21–24, 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 \({H_0}\)?

Short Answer

Expert verified

a.The critical value is equal to -1.645.

b.The null hypothesis is rejected.

Step by step solution

01

Given information

A test statistic value of \(z = - 2.50\) is obtained, and the claim to be tested is \(p < 0.75\).

02

Hypotheses and tail of the test

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

Null Hypothesis:\(p = 0.75\)

Alternative Hypothesis:\(p < 0.75\)

Since there is a lesser than sign in the alternative hypothesis, the test is left-tailed.

03

Critical value

a.

Referring to the standard normal table, the critical value of z corresponding to the left-tailed test at \(\alpha = 0.05\) is equal to -1.645.

04

Decision about the test

b.

If the absolute value of the test statistic is greater than the critical value, then the null hypothesis is rejected.

Here, the absolute value of the test statistic (2.50) is greater than the critical value (-1.645). Thus, the null hypothesis is rejected.

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Most popular questions from this chapter

Finding P-values. In Exercises 5–8, either use technology to find the P-value or use Table A-3 to find a range of values for the P-value.

8. Tornadoes. The claim is that for the widths (yd) of tornadoes, the mean is μ<140 yd. The sample size is n = 21 and the test statistic is t = -0.024.

Using Technology. In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use α= 0.05 significance level and answer the following:

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?

Self-Driving Vehicles In a TE Connectivity survey of 1000 adults, 29% said that they would feel comfortable in a self-driving vehicle. The accompanying StatCrunch display results from testing the claim that more than 1/4 of adults feel comfortable in a self-driving vehicle.

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.

Requirements and Conclusions

a. Are any of the three requirements violated? Can the methods of this section be used to test the claim?

b. It was stated that we can easily remember how to interpret P-values with this: “If the P is low, the null must go.” What does this mean?

c. Another memory trick commonly used is this: “If the P is high, the null will fly.” Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading?

d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like 0.0483?

P-Values. In Exercises 17–20, do the following:

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value. (See Figure 8-3 on page 364.)

c. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

The test statistic of z = -1.94 is obtained when testing the claim that p=38 .

Confidence interval Assume that we will use the sample data from Exercise 1 “Video Games” with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing the claim, what confidence level should be used for the confidence interval? If the confidence interval is found to be 21.1 sec < μ< 191.4 sec, what should we conclude about the claim?
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