the critical value for a lower-tailed test from a sample of 32 at a.025 level of significance is (use 3 decimal places)

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1 1. With the population variance known, the critical value of a lower-tailed test at a 0.05 level of significance is (use 3 decimal places). the critical value of an upper-tailed test at a 0.05 level of significance is (use 3 decimal places). the critical values of a two-tailed test at a 0.01 level of significance are (, ) (use 3 decimal places). 2. With the population standard deviation unknown, the critical value for a lower-tailed test from a sample of 32 at a.025 level of significance is (use 3 decimal places) the critical value for an upper-tailed test from a sample of 32 at a.05 level of significance is (use 3 decimal places) the critical values for a 2-tailed test from a sample of 32 at a.10 level of significance is (, ) (use 3 decimal places) 3. In random sample of 60 with the mean equal to 42, you want to test whether the average is 50. Assume the population standard deviation is 28. The test statistic equals (use 3 decimal places), at 5% significance. Thus,. In random sample of 40 with the mean equal to 51, you want to test whether the average is significantly more than 50. Assume the population standard deviation is 28. The test statistic equals (use 3 decimal places), at 5% significance. Thus,. In random sample of 35 with the mean equal to 45, you want to test whether the average is significantly less than 50. Assume the population standard deviation is 28. The test statistic equals (use 3 decimal places), at 5% significance. Thus,.

2 4. Consider the following hypothesis test: H0: μ > 20 Ha: μ < 20 A sample of 55 provided a sample mean of The population standard deviation is 1.6. Compute the value of the test statistic (to 4 decimals). Using α = 0.1, what is the critical value for the test statistic (to 3 decimals)? State the rejection rule: Reject H0 if the test statistic is the critical value. Using α = 0.1, can it be concluded that the population mean is less than 20? 5. Consider the following hypothesis test: H0: μ < 50 Ha: μ > 50 A sample of 68 is used and the population standard deviation is 7.6. Use the critical value approach to state your conclusion for each of the following sample results. With α = 0.01, the critical value is With the sample mean = 52.5, what is the value of the test statistic (to 4 decimals)? With the sample mean = 51.8, what is the value of the test statistic (to 4 decimals)? With sample mean = 51.0, what is the value of the test statistic (to 4 decimals)?

3 6. Wall Street securities firms paid out record year-end bonuses of $ per employee for 2005 (Fortune, February 6, 2006). We would like to take a sample of employees at the Jones & Ryan securities firm to see whether the mean year-end bonus is different from $125,500. A random sample of 40 employees at Jones & Ryan yielded an average year-end bonus of $ Assume a population standard deviation of $ The null and alternative hypotheses are H0: μ With α = 0.02 as the level of significance, the critical values for the test statistic are +/- (use 3 decimal places). The test statistic equals (use 4 decimal places). Can you reject the null hypothesis? Thus, you. 7. In 2001, the U.S. Department of Labor reported the average hourly earnings for U.S. production workers to be $14.32 per hour (The World Almanac 2003). A sample of 54 production workers during 2003 showed a sample mean of $14.26 per hour. Assuming the population standard deviation is $2.05, can we conclude that an increase occurred in the mean hourly earnings since 2001? State the hypotheses. H0: μ The text statistic equals (use 4 decimal places). Using α = 0.1, the critical value equals (use 3 decimal places). Can you conclude that there has been an increase in the population mean hourly wage of production workers? 8. Consider the following hypothesis test: H0: μ > 20 Ha: μ < 20 A sample of 34 provided a sample mean of and a standard deviation of Compute the value of the test statistic (to 4 decimals). Using α = 0.1, what is the critical value for the test statistic (to 3 decimals)? State the rejection rule: Reject H0 if the test statistic is the critical value. Using α = 0.1, can it be concluded that the population mean is less than 20?

4 9. Consider the following hypothesis test: H0: μ < 50 Ha: μ > 50 Samples of size 53 are used to test the hypotheses above. With α = 0.02, the critical value is With the sample mean = 52.5 and sample standard deviation = 7.74, what is the value of the test statistic (to 4 decimals)? With the sample mean = 51.8 and sample standard deviation = 7.92, what is the value of the test statistic (to 4 decimals)? With sample mean = 51.0 and sample standard deviation = 8.71, what is the value of the test statistic (to 4 decimals)? 10. Wall Street securities firms paid out record year-end bonuses of $125,500 per employee for 2005 (Fortune, February 6, 2006). We would like to take a sample of employees at the Jones & Ryan securities firm to see whether the mean year-end bonus is different from $125,500. A random sample of 34 employees at Jones & Ryan yielded an average year-end bonus of $ and a standard deviation of $ The null and alternative hypotheses are H0: μ With α = 0.05 as the level of significance, the critical values for the test statistic are +/- (use 3 decimal places). The test statistic equals (use 4 decimal places). Can you reject the null hypothesis? Thus, you.

5 11. In 2001, the U.S. Department of Labor reported the average hourly earnings for U.S. production workers to be $14.32 per hour (The World Almanac 2003). A sample of 42 production workers during 2003 showed a mean of $13.84 per hour and a standard deviation of $2.57 per hour. Can we conclude that an increase occurred in the mean hourly earnings since 2001? State the hypotheses. H0: μ The text statistic equals (use 4 decimal places). Using α = 0.05, the critical value equals (use 3 decimal places). Can you conclude that there has been an increase in the population mean hourly wage of production workers? 12. Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 113 individuals from the Midwestern town of Webster City showed a mean annual consumption of 22.3 gallons and a variance of The hypotheses for this test are H0: μ At 10% significance, the critical value for this test is (to 3 decimals). The value of the test statistic (to 4 decimals). We. 13. The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of $238 per week (The World Almanac 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level. The hypotheses for this test are H0: μ A sample of 127 individuals had a mean weekly unemployment insurance benefit of $ and a variance of The test statistic is (to 4 decimal places). At 2.5% significance, the critical value of the test is (to 3 decimal places). What is the conclusion of this test? Thus, we

6 14. Your firm has been hired by Senator Smith to poll likely voters. The following hypothesis test is used to determine support for the Senator. H0: p > 0.5 Ha: p < 0.5 At 10% significance, the critical value for the test statistic is (to 3 decimals). If 50.6% of 141 voters surveyed by your firm support Senator Smith's presidential campaign, the test statistic equals (to 4 decimals). The null hypothesis Thus, we This suggests that If 50.6% of 1721 voters surveyed by your firm support Senator Smith's presidential campaign, the test statistic equals (to 4 decimals). The null hypothesis Thus, we This suggests that Which of the following statements is true: Which of the following statements is true: 15. Your firm has been hired by the Quartz Computer Corporation to determine if a majority of Americans are aware of it its notebook computers. The hypotheses for this test are H0: p Ha: p At 10% significance, the critical value for the test statistic is (to 3 decimals). If 47.6% of 303 consumers surveyed by your firm are aware of it its notebook computers, the test statistic equals (to 4 decimals). Given the results of this test, the null hypothesis Thus, we.

7 16. Suppose the nation's employment-to-population ratio (epr) is 63%. You would like to know if your county's epr is the same as the national epr. The hypotheses for this test are H0: p Ha: p At 10% significance, the critical values for the test statistic are +/- (to 3 decimals). If 63.5% of 437 people in your county's work force are employed, the test statistic equals (to 4 decimals). The null hypothesis Thus, we