INTRO:

QUESTION 1 a) 1. Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondents general attitude toward each of the three shopping areas. Each of these variables has numerically equal distances between the possible responses, and for purposes of analysis they may be considered to be of the interval scale of measurement. a. Determine the point estimate, then construct the 95% confidence interval for pi28= the population average attitude toward Springdale Mall. What is the maximum likely error in the point estimate of the population mean?

INTEGRATED CASES Thorndike Sports Equipment (Thorndike Video Unit Four) Seeing the fishing pole in his grandfather's office, Ted The elder Thorndike explains, "Ted, this fishing pole is Thorndike's first thought is that old Luke is going to made of graphite, the same stuff that goes into our Graf-Pro go fishing again and leave him to manage the store. He racquetball racquets. It's so flexible and strong that it can be is quite surprised to learn the fishing pole is actually bent so the two ends actually touch each other. They even an inspiration for a new series of ads that Luke has in show this in the ads." Although Luke realizes that you can't mind. do exactly the same thing with a racquetball racquet, he'd (continued) 308 Part 3: Sampling Distributions and Estimation like to put some of his racquets into a horizontal mounting For 20 racquets subjected to this severe test, the weight device, then see how much weight they'll take before they (in pounds) at which each one failed was as follows. The break. data are also in file THORN09. If the amount of weight is impressive enough, Luke plans to include this kind of test in the television adver 221 228 223 218 218 tisements he's planning for the firm's racquetball racquets. 208 220 217 224 225 However, he wants to be careful not to brag about the 224 222 229 215 221 racquer being able to hold too much weight, since the 217 230 236 222 234 firm could get into trouble with the government and other truth-in-advertising advocates. Ted believes it's reasonable to assume the population He asks Ted to set up a test in which racquets are of breaking strengths is approximately normally distrib- mounted horizontally, then the weight on the end is uted. Because of Luke's concern about being able to sup- gradually increased until they break. Based on the test re- port the advertising claim, he wants to be very conservative sults, a weight value would be selected such that the aver. in estimating the population mean for these breaking age racquet would almost certainly be able to withstand strengths. Ted needs some help in deciding how conserva- this amount. Although accuracy is important, Ted has tive he would like to be, and in coming up with a number been instructed not to break more than 15 or 20 racquets that can be promoted in the ads. in coming up with an average for all the racquets. Springdale Shopping Survey The case in Chapter 2 listed 30 questions asked of 150 and for purposes of analysis they may be considered to respondents in the community of Springdale. The coding be of the interval scale of measurement key for the responses was also provided in that earlier a. Determine the point estimate, then construct the exercise. The data are in file SHOPPING. In this exercise, 95% confidence interval for fly - the average some of the estimation techniques presented in the chapter attitude toward Springdale Mall. What is the maxi- will be applied to the survey results. You may assume that mum likely error in the point estimate of the popu- these respondents represent a simple random sample of all lation mean? potential respondents within the community and that the b. Repeat part (a) for us and this, the average population is large enough that application of the finite attitudes toward Downtown and West Mall, population correction would not make an appreciable dif respectively. ference in the results. 2. Given the breakdown of responses for variable 26 Managers associated with shopping areas like these (sex of respondent), determine the point estimate, find it useful to have point estimates regarding variables then construct the 95% confidence interval for #26 describing the characteristics and behaviors of their cus the population proportion of males. What is the tomers. In addition, it is helpful for them to have some maximum likely crror in the point estimate of the idea as to the likely accuracy of these estimates. Therein population proportion? lies the benefit of the techniques presented in this chapter 3. Given the breakdown of responses for variable 28 and applied here. (marital status of respondent), determine the point 1. Item in the description of the data collection instru- estimate, then construct the 95% confidence interval ment lists variables 7, 8, and 9, which represent the for Tyx = the population proportion in the "single or respondent's general attitude toward each of the three other" category. What is the maximum likely error in the point estimate of the population proportion? shopping areas. Each of these variables has numeri- cally equal distances between the possible responses