BackAtkins 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 mean weight loss for all such subjects. Does the Atkins program appear to be effective? Does it appear to be practical?
Archeology Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the widths (mm) of skulls from 150 A.D. (based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver). Construct a 99% confidence interval estimate of the mean skull width.
Minting Quarters Listed below are weights (grams) of quarters minted after 1964 (based on Data Set 40 “Coin Weights” in Appendix B). Construct a 95% confidence interval estimate of the mean weight of all quarters minted after 1964. Specifications require that the quarters have a weight of 5.670 g. What does the confidence interval suggest about that specification?
Los Angeles Commute Time Listed below are 15 Los Angeles commute times (based on a sample from Data Set 31 “Commute Times” in Appendix B). Construct a 99% confidence interval estimate of the population mean. Is the confidence interval a good estimate of the population mean?
Genes Samples of DNA are collected, and the four DNA bases of A, G, C, and T are coded as 1, 2, 3, and 4, respectively. The results are listed below. Construct a 95% confidence interval estimate of the mean. What is the practical use of the confidence interval?
2 2 1 4 3 3 3 3 4 1
Mercury in Sushi An FDA guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D’Agostino, Eli’s Manhattan, Fairway, Food Emporium, Gourmet Garage, Grace’s Marketplace, and Whole Foods. Construct a 98% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?
0.56 0.75 0.10 0.95 1.25 0.54 0.88
Quarters Assume that weights of quarters minted after 1964 are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g (based on U.S. Mint specifications).
b. If 25 quarters are randomly selected, find the probability that their mean weight is greater than 5.675 g.
Requirements A construction quality control analyst has collected a random sample of six concrete road barriers, and she plans to weigh each of them and construct a 95% confidence interval estimate of the mean weight of all such barriers. What requirements must be satisfied in order to construct the confidence interval with the method from Section 7-2 that uses the t distribution?
Degrees of Freedom In general, what does “degrees of freedom” refer to? For the sample data described in Exercise 7 “Requirements,” find the number of degrees of freedom, assuming that you want to construct a confidence interval estimate of u using the t distribution.
Space Mountain Use the following wait times (minutes) for the Space Mountain ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B). Construct a 95% confidence interval estimate of the mean of all wait times. Write a brief statement that interprets that confidence interval.
40 35 40 40 25 80 50 30 35 40
In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used.
Refer to the accompanying screen display.
a. Express the confidence interval in the format that uses the “less than” symbol. Round the confidence interval limits given that the original times are all rounded to one decimal place.
In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used.
Degrees of Freedom
a. What is the number of degrees of freedom that should be used for finding the critical value ta/2?
In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used.
Degrees of Freedom
b. Find the critical value ta/2 corresponding to a 95% confidence level.
In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used.
Interpreting a Confidence Interval The results in the screen display are based on a 95% confidence level. Write a statement that correctly interprets the confidence interval.
In Exercises 5–8, (a) identify the critical value ta/2 used for finding the margin of error, (b) find the margin of error, (c) find the confidence interval estimate of u, and (d) write a brief statement that interprets the confidence interval.
Birth Weights Here are summary statistics for randomly selected weights of newborn girls: n=36, x=3150.0g, s=695.5g (based on Data Set 6 “Births” in Appendix B). Use a confidence level of 95%.