Use a computer program to obtain 1,000 bootstrap samples from the 8 oxygen levels.

5.9 Inferences about the Median 5.52 Suppose we have a random sample of n ⫽ 15 measurements from a population having population median M. The research design calls for a 95 confidence interval on M.

a. Use Table 4 in the Appendix to obtain L

a 兾2 and U a 兾2 .

b. Use the large-sample approximation to determine L

a 兾2 and U a 兾2 . Compare these val- ues to the values obtained in part a. 5.53 Suppose we have a random sample of n ⫽ 45 measurements from a population having population median M. The research design calls for a 95 confidence interval on M.

a. Use Table 4 in the Appendix to obtain L

a 兾2 and U a 兾2 .

b. Use the large-sample approximation to determine L

a 兾2 and U a 兾2 . Compare these values to the values obtained in part a. 5.54 A researcher selects a random sample of 30 units from a population having a median M. Construct the rejection region for testing the research hypothesis H a : M ⬎ M using a ⫽ .01 and values in Table 4 of the Appendix. 5.55 Refer to Exercise 5.54. Use the large-sample approximation to set up the rejection region for testing the research hypothesis H a : M ⬎ M using a ⫽ .01. Compare this rejection region to the rejection region obtained in Exercise 5.54. Bus. 5.56 The amount of money spent on health care is an important issue for workers because many companies provide health insurance that only partial covers many medical procedures. The direc- tor of employee benefits at a midsize company wants to determine the amount spent on health care by the typical hourly worker in the company. A random sample of 25 workers is selected and the amount they spent on their families’ health care needs during the past year is given here. 400 345 248 1,290 398 218 197 342 208 223 531 172 4,321 143 254 201 3,142 219 276 326 207 225 123 211 108

a. Graph the data using a boxplot or normal probability plot and determine whether the

population has a normal distribution.

b. Based on your answer to part a, is the mean or the median cost per household a

more appropriate measure of what the typical worker spends on health care needs?

c. Place a 95 confidence interval on the amount spent on health care by the typical

worker. Explain what the confidence interval is telling us about the amount spent on health care needs. d. Does the typical worker spend more than 400 per year on health care needs? Use a ⫽ .05. Gov. 5.57 Many states have attempted to reduce the blood-alcohol level at which a driver is declared to be legally drunk. There has been resistance to this change in the law by certain business groups who have argued that the current limit is adequate. A study was conducted to demonstrate the effect on reaction time of a blood-alcohol level of .1, the current limit in many states. A ran- dom sample of 25 persons of legal driving age had their reaction time recorded in a standard labo- ratory test procedure before and after drinking a sufficient amount of alcohol to raise their blood alcohol to a .1 level. The difference After − Before in their reaction times in seconds was recorded as follows: .01 .02 .04 .05 .07 .09 .11 .26 .27 .27 .28 .28 .29 .29 .30 .31 .31 .32 .33 .35 .36 .38 .39 .39 .40 a. Graph the data and assess whether the population has a normal distribution. b. Place a 99 confidence interval on both the mean and median difference in reaction times of drivers who have a blood-alcohol level of .1.

c. Is there sufficient evidence that a blood-alcohol level of .1 causes any increase in

the mean reaction time?

d. Is there sufficient evidence that a blood-alcohol level of .1 causes any increase in

the median reaction time?

e. Which summary of reaction time differences seems more appropriate, the mean or

median? Justify your answer.