1- ConsiderH0:=72 versusH1:>72. A random sample of16observations taken from this population produced a sample mean of75.7. The population is normally distributed with=6.

a.Calculate thep-value. Round your answer to four decimal places.

b.Considering thep-value of parta., would you reject the null hypothesis if the test were made at the significance level of0.01?

c.Considering thep-value of parta., would you reject the null hypothesis if the test were made at the significance level of0.025?

2-A random sample of140observations produced a sample mean of33. Find the critical and observed values ofzfor the following test of hypothesis using=0.01.The population standard deviation is known to be5and the population distribution is normal. H0:=28 versusH1:28. Round your answers to two decimal places.

3-A random sample of130observations produced a sample mean of31. Find the critical and observed values ofzfor the following test of hypothesis using=0.1. The population standard deviation is known to be6and the population distribution is normal. H0:=28versusH1:>28. Round your answers to two decimal places.

4-The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is45months. A consumer protection agency that wants to check this claim took a random sample of24such batteries and found that the mean life for this sample is43.30months. The lives of all such batteries have a normal distribution with the population standard deviation of4.5months. Find thep-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than45months. Round your answer to four decimal places.

5-A random sample of11observations taken from a population that is normally distributed produced a sample mean of42.4and a standard deviation of8. Find the range for thep-value and the critical and observed values oftfor each of the following tests of hypotheses using,=0.01. Use thetdistribution table to find a range for thep-value. Round your answers for the values oftto three decimal places.

a.H0:=46 versusH1:<46.

b.H0:=46 versusH1:46.

6-According to an estimate, the average total parent and student debt for new college graduates was $34,400in 2010-11 (Time, October 31, 2011). A random sample of455of this year's graduates showed that their average such debt is $38,000with a standard deviation of $5530. Do the data provide significant evidence at a10% significance level to conclude that the current average total parent and student debt for new graduates is higher than $34,400? Use both thep-value approach and the critical-value approach. Use thep-value approach. Use thetdistribution table to find a range for thep-value. Enter the exact values for the range. Use the critical-value approach. Round your observed value to four decimal places, and your critical value to two d

7-According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY, June 30, 2011). Suppose that in a recent sample of1580children,242were found to be living with at least one grandparent. At a2.5% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%? Use both thep-value and the critical-value approaches. Round your answers for the observed value ofzand the critival value ofzto two decimal places, and thep-value to four decimal places.

8- According to aNew York Times/CBS News poll conducted during June 24-28, 2011, 55% of the American adults polled said that owning a home is avery important partof the American Dream (The New York Times, June 30, 2011). Suppose this result was true for the population of all American adults in 2011. In a recent poll of1790American adults,62% said that owning a home is avery important partof the American Dream. Perform a hypothesis test to determine whether it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%. Use a5% significance level, and use both thep-value and the critical-value approaches. Round your answers for the observed value ofzand the critical value ofzto two decimal places, and thep-value to four decimal places.

9- For the following significance level, what is the probability of making a Type I error? =0.1

10- Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not produce each rod exactly 36 inches long. The lengths of the rods are normally distributed and vary slightly. It is known that when the machine is working properly, the mean length of the rods is 36 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.035 inch. The quality control department at the company takes a sample of 20 such rods every week, calculates the mean length of these rods, and tests the null hypothesis,=36 inches, against the alternative hypothesis,36 inches. If the null hypothesis is rejected, the machine is stopped and adjusted. A recent sample of 20 rods produced a mean length of 36.015 inches. Calculate thep-value for this test of hypothesis. Based on thisp-value, will the quality control inspector decide to stop the machine and adjust it if he chooses the maximum probability of a Type I error to be0.025?

Use the normal distribution table. Round your answer to four decimal places.

11-According to a Pew Research Center nationwide telephone survey of adults conducted between March 15 and April 24, 2011, 55% of college graduates said that college education prepared them for a job (Time, May 30, 2011). Suppose this result was true of all college graduates at that time. In a recent sample of1850college graduates,60% said that college education prepared them for a job. Is there significant evidence at a2% significance level to conclude that the current percentage of all college graduates who will say that college education prepared them for a job is different from 55%? Use both thep-value and the critical-value approaches. Round your answers for the observed value ofzand the critical value ofzto two decimal places, and thep-value to four decimal places. Enter the critical values in increasing order.

12-A random sample of20observations taken from a population that is normally distributed produced a sample mean of58.5and a standard deviation of7.5. Find the range for thep-value and the critical and observed values oftfor the following test of hypothesis, using=0.01. H0:=55

versusH1:55. Round your answers for the values oftto three decimal places.

13- A random sample of27observations taken from a population that is normally distributed produced a sample mean of58.5and a standard deviation of7.5. Find the range for thep-value and the critical and observed values oftfor the following test of hypothesis, using=0.01. H0:=55

versusH1:>55. Use thetdistribution table to find a range for thep-value. Round your answers for the values oftto three decimal places.

14-A random sample of14observations taken from a population that is normally distributed produced a sample mean of42.4and a standard deviation of8. Find the range for thep-value and the critical and observed values oftfor each of the following tests of hypotheses using,=0.01.

Use thetdistribution table to find a range for thep-value. Round your answers for the values oftto three decimal places.

a.H0:=46 versusH1:<46.

b.H0:=46 versusH1:46.

15-A random sample of580observations produced a sample proportion equal to0.33. Find the critical and observed values ofzfor the following test of hypotheses using=0.1. H0:p=0.30 versusH1:p>0.30. Round your answers to two decimal places.

16-A random sample of510observations produced a sample proportion equal to0.36. Find the critical and observed values ofzfor the following test of hypotheses using=0.1. H0:p=0.30 versusH1:p0.30. Round your answers to two decimal places.