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Chapter 8: Q. 9.77 (page 380)

We have been provided a sample mean, sample size, and population standard deviation. In the given case, use the one-mean z-test to perform the required hypothesis test at the 5%significance level.

x¯=20,n=32,σ=4,H0:μ=22,Ha:μ<22

Short Answer

Expert verified

The value ofzis-2.83, critical value is-1.645,P=0.002and rejectH0.

Step by step solution

01

Step 1. Given information.

Consider the given question,

x¯=20,n=32,σ=4,H0:μ=22,Ha:μ<22

02

Step 2. Consider the test hypothesis.

Consider the given hypothesis,

μis the population mean.

The test hypothesis,

Ho:μ=22vs

Ha:μ<22

Therefore, the test is left tailed test.

And the level of significance is α=0.05.

03

Step 3. Use the test statistics.

We want to find the hypothesis test about the mean μ,

z=x¯-μ0σn=20-22432=-2.83

Therefore, this is left tailed test with α=0.05, the critical value is given below,

-za=-z0.05=-1.645

The rejection region is z<-z0.05.

Here, z=-2.83<-z0.05=-1.645

Hence, we reject Hoat 5% level of significances the value of the test statistic z falls in the rejection region.

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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.

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 α = 0.05, should we reject H0or should we fail to reject H0?

The test statistic of z = 2.01 is obtained when testing the claim that p≠0.345.

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. 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.

Car Booster Seats The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement?

774 649 1210 546 431 612

Technology. In Exercises 9–12, 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.

Body Temperatures Data Set 3 “Body Temperatures” in Appendix B includes 93 body temperatures measured at 12 ²³ on day 1 of a study, and the accompanying XLSTAT display results from using those data to test the claim that the mean body temperature is equal to 98.6°F. Conduct the hypothesis test using these results.

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 α= 0.05, should we reject or should we fail to reject ?

The test statistic of z = 1.00 is obtained when testing the claim that p>0.3.
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