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Chapter 9: Q.10 (page 392)

Determine the critical value(s) for a one-mean z-test at the 1 % significance level if the test is

a. right tailed.

b. left tailed.

c. two tailed.

Short Answer

Expert verified

(a) Since 伪=0.01. The critical value of z0.01=2.33is found in normal distribution tables, as illustrated in the image.

(b) Since 伪=0.01. The critical value of -z0.01=-2.33is found in normal distribution tables, as illustrated in the image.

(c) Since 伪=0.01. The critical value of 卤z0.012=卤z0.005=2.575is found in normal distribution tables, as illustrated in the image.

Step by step solution

01

Subpart (a) Step 1:

(a)

If the test is right tailed, we find the crucial value for a one-mean z-test at the 1% significance level.

Since 伪=0.01. The critical value of z0.01=2.33is found in normal distribution tables, as illustrated in the image.

02

Subpart (b) Step 1:

(b)

If the test is right tailed, we find the crucial value for a one-mean z-test at the 1% significance level.

Since 伪=0.01. The critical value of -z0.01=-2.33is found in normal distribution tables, as illustrated in the image.

03

Subpart (c) Step 1:

(c)

If the test is right tailed, we find the crucial value for a one-mean z-test at the 1% significance level.

Since 伪=0.01. The critical value of 卤z0.012=卤z0.005=卤2.575is found in normal distribution tables, as illustrated in the image.

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Most popular questions from this chapter

In the article "Business Employment Dynamics: New data on Gross Job Gains and Losses", J. Spletzer et al. examined gross job gains and losses as a percentage of the average of previous and current employment figures. A simple random sample of 20quarters provided the net percentage gains for jobs as presented on the WeissStats site. Use the technology of your choice to do the following.

Part (a): Decide whether, on average, the net percentage gain for jobs exceeds 0.2. Assume a population standard deviation of 0.42. Apply the one-mean z-test with a 5%significance level.

Part (b): Obtain a normal probability plot, boxplot, histogram and stem-and-leaf diagram of the data.

Part (c): Remove the outliers from the data and then repeat part (a).

Part (d): Comment on the advisability of using thez-test here.

9.95 Two-Tailed Hypothesis Tests and CIs. As we mentioned on page 378 , the following relationship holds between hypothesis tests and confidence intervals for one-mean z-procedures: For a two-tailed hypothesis test at the significance level 伪, the null hypothesis H0:渭=渭0 will be rejected in favor of the alternative hypothesis Ha:渭鈮�渭0if and only if 渭0 lies outside the (1-伪)-level confidence interval for 渭. In each case, illustrate the preceding relationship by obtaining the appropriate one-mean z-interval (Procedure 8.1 on page 322 ) and comparing the result to the conclusion of the hypothesis test in the specified exercise.
a. Exercise 9.84
b. Exercise 9.87

Purse Snatching. The Federal Bureau of Investigation (FBI) compiles information on robbery and property crimes by type and selected characteristic and publishes its findings in Uniform Crime Reports. According to that document, the mean value lost to purse snatching was 468in 2012. For last year, 12randomly selected purse-snatching offenses yielded the following values lost, to the nearest dollar.

Use a t-test to decide, at the5%significance level, whether last year's mean value lost to purse snatching has decreased from the 2012mean. The mean and standard deviation of the data are 455.0and 86.8, respectively.

The normal probability curve and histogram of the data are shown in figure; 蟽is known.

Perform Hypothesis test for mean of the population from which data is obtained and decide whether to use z-test, t-test or neither. Explain your answer.

The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a two-tailed hypothesis test at the significance level 伪, the null hypothesis H0:渭=渭0will be rejected in favor of the alternative hypothesis Ha:渭>渭0if and only if 渭0lies outside the 1-伪-level confidence interval for 渭. In each case, illustrate the preceding relationship by obtaining the appropriate one-mean t-interval and comparing the result to the conclusion of the hypothesis test in the specified exercise.

Part (a): Exercise 9.113

Part (b): Exercise 9.116
See all solutions

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