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1.The data in the table are the diameters and heights of 10 fossil specimens of a species of small shellfish that were unearthed in a mapping expedition near the Antarctic Peninsula.16 The table gives an identification symbol for the fossil specimen, the fossil’s diameter and height in millimeters, and the ratio of diameter to height.
a. Find a 95% confidence interval for the mean diameter of the species.
b. Find a 95% confidence interval for the mean height of the species.
c. Find a 95% confidence interval for the mean ratio of diameter to height.
d. Compare the three intervals constructed in parts a, b and c. Is the average of the ratios the same as the ratio of the average diameter to average height?
2. Refer to Exercise 1. Suppose you want to estimate the mean diameter of the fossil specimens correct to within 5 millimeters with probability equal to .95. How many fossils do you have to include in your sample?
3. Researchers examined the differences in a particular plant when grown in full sunlight versus shade conditions. In this study, shaded plants received direct sunlight for less than 2 hours each day, whereas full-sun plants were never shaded. A partial summary of the data based on n shade plants is shown here.
a. What assumptions are required in order to use the small-sample procedures given in this chapter to compare full-sun versus shade plants? From the summary presented, do you think that any of these assumptions have been violated?
b. Do the data present sufficient evidence to indicate a difference in mean leaf area for full-sun versus shade plants?
c. Do the data present sufficient evidence to indicate a difference in mean overlap area for full-sun versus shade plants?
4. Many seniors are ordering their drugs online to take advantage of lower costs for these pharmacies. A random sample of nine online pharmacies was selected and the cost of a 10-mg Buspirone tablet recorded, as given in the following table.
a. Test the hypothesis of no difference in costs between brand and generic Buspirone 10-mg tablets at the a5.05 level of significance. (hint: the observations are paired by the online pharmacies.)
b. Find the estimated savings per tablet by purchasing the generic as opposed to the brand-name tablets with a 95% confidence interval.
5. The following data are the response times in seconds for n525 first graders to arrange three objects by size.
Find a 95% confidence interval for the average response time for first graders to arrange three objects by size. Interpret this interval.
6. Want to attend a pro basketball game? The average resale prices for the NBA rematch of the Cleveland Cavaliers and the Golden State Warriors in 2017 compared to the average ticket prices in 2016 are given in the table that follows.
a. If we were to assume that the prices given in the table have been randomly selected, test for a signifi-cant difference between the 2016 and the 2017 prices using a = .01.
b. Find a 99% confidence interval for the mean difference µd= µ2016- µ2017. Does this estimate confirm the results in part a?
 
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