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Chapter 9: Q. 13 (page 392)
Define the- value of the hypothesis test.
The \(P-\)value is the probability that the data from the sample is inconsistent with the null hypothesis.
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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.
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 significance level.
As we mentioned on page 378, the following relationship holds between hypothesis test and confidence intervals for one-mean z-procedures: For a two-tailed hypothesis test at the significance level , the null hypothesis role="math" localid="1653038937481" will be rejected in favor of the alternative hypothesis if and only if lies outside the -level confidence interval for . In each case, illustrate the preceding relationship by obtaining the appropriate one-mean z-interval and comparing the result to the conclusion of the hypothesis test in the specified exercise.
Part (a): Exercise 9.84
Part (b): Exercise9.87
Refer to Problem 24.The following table provides last year's cheese consumption, in pounds, for 35 randomly selected Americans.
Part (a): At the 10%significance level, do the data provide sufficient evidence to conclude that last year's mean cheese consumption for all Americans has increased over the 2010 mean? Assume that . Use a z-test.
Part (b): Given the conclusion in part (a), if an error has been made, what type must it be? Explain your answer.
9.89 Job Gains and Losses. In the article "Business Employment Dynamics: New Data on Gross Job Gains and Losses" (Monthly Labor Review, Vol. 127. Issue 4. pp. 29-42). 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 20 quarters provided the net percentage gains (losses are negative gains) for jobs as presented on the WeissStats site. Use the technology of your choice to do the following.
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 significance level.
b. Obtain a normal probability plot, boxplot, histogram, and stem-and-leaf diagram of the data.
c. Remove the outliers (if any) from the data and then repeat part (a).
d. Comment on the advisability of using the z-test here.
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