BackDetermining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped.
Taxi Trips The distances (miles) traveled by New York City taxis transporting customers, as listed in Data Set 32 “Taxis” in Appendix B
Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped.
Dunkin’ Donuts The drive-through service times (seconds) of Dunkin’ Donuts lunch customers, as listed in Data Set 36 “Fast Food” in Appendix B
Good Sample? An economist is investigating the incomes of college students. Because she lives in Maine, she obtains sample data from that state. Is the resulting mean income of college students a good estimator of the mean income of college students in the United States? Why or why not?
Distributions Identify the distribution (normal, Student t, chi-square) that should be used in each of the following situations. If none of the three distributions can be used, what other method could be used?
a. In constructing a confidence interval of , you have 75 sample values and they appear to be from a population with a skewed distribution. The population standard deviation is not known.
Atkins Weight Loss Program In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 90% confidence interval estimate of the standard deviation of the weight loss for all such subjects. Does the confidence interval give us information about the effectiveness of the diet?
Arm Circumferences Listed below are arm circumferences (cm) of randomly selected women (based on Data Set 1 “Body Data” from Appendix B). Also shown is the normal quantile plot of those measurements.
b. Are the requirements for constructing a 95% confidence interval estimate of the population standard deviation satisfied? If so, construct that confidence interval.
Degrees of Freedom For Example 1, we used df=smaller of n1-1 and n2-1 we got df=11 and the corresponding critical value is t=-1.796 (found from Table A-4). If we calculate df using Formula 9-1, we get df=19.370 and the corresponding critical value is t=-1.727 How is using the critical value of t=-1.796 “more conservative” than using the critical value of t=-1.727
Alcohol in Children’s Movies Listed below is a simple random sample of times (seconds) that animated children’s movies showed the use of alcohol (based on Data Set 20 “Alcohol and Tobacco in Movies” in Appendix B).
a. Are the requirements for constructing a 95% confidence interval estimate of the population mean satisfied? If so, construct that confidence interval.
Tour de France Listed below are the average speeds (km/h) of winners of the Tour de France men’s bicycle race. The speeds are listed in order by year, beginning with the year 2000.
a. Construct a 95% confidence interval estimate of the population mean.
Pulse Rates of Women and Men Using the samples of women and men included in Data Set 1 “Body Data,” we get this 95% confidence interval estimate of the difference between the population mean of pulse rates (bpm) of women and the population mean of pulse rates (bpm) of men: 1.7 bpm < u1-u2 < 7.2bpm. In this confidence interval, women correspond to population 1 and men correspond to population 2.
a. What does the confidence interval suggest about equality of the mean pulse rate of women and the mean pulse rate of men?
Large Data Sets from Appendix B. In Exercises 21 and 22, use the data set in Appendix B. Assume that each sample is a simple random sample obtained from a population with a normal distribution.
Birth Weights Refer to Data Set 6 “Births” in Appendix B.
a. Use the 205 birth weights of girls to construct a 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained.
FINDING SAMPLE SIZE Instead of using Table 7-2 for determining the sample size required to estimate a population standard deviation σ, the following formula can also be used
where corresponds to the confidence level and d is the decimal form of the percentage error. For example, to be 95% confident that s is within 15% of the value of σ, use zα/2=1.96 and d=0.15 to get a sample size of n=86. Find the sample size required to estimate the standard deviation of IQ scores of data scientists, assuming that we want 98% confidence that s is within 5% of σ.
7. FRESHMAN 15 Here is a sample of amounts of weight change (kg) of college students in their freshman year (from Data Set 13 “Freshman 15” in Appendix B): 11, 3, 0, –2, where –2 represents a loss of 2 kg and positive values represent weight gained. Here are ten bootstrap samples:
{11, 11, 11, 0}, {11, –2, 0, 11}, {11, –2, 3, 0}, {3, –2, 0, 11}, {0, 0, 0, 3}, {3, –2, 3, –2}, {11, 3, –2, 0}, {–2, 3, –2, 3}, {–2, 0, –2, 3}, {3, 11, 11, 11}.
b. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the standard deviation of the weight changes for the population.
15. HEIGHTS OF FEMALE SOCCER PLAYERS Listed below are the heights (in.) of players on the U.S. Women’s National Soccer Team (at the time of this writing). Use those heights as a sample of the heights of all professional women soccer players.
a. Use 1000 bootstrap samples to construct a 95% confidence interval estimate of σ.
Mint Specs Listed below are weights (grams) from a simple random sample of pennies produced after 1983 (from Data Set 40 “Coin Weights” in Appendix B).
b. How does the result compare to the confidence interval found in Exercise 14 in Section 7-3?