Question.3179 - 10.7 According to a recent study, when shopping online for luxury goods, men spend a mean of $2,401, whereas women spend a mean of $1,527 (data extracted from R. A. Smith, “Fashion Online: Retailers Tackle the Gender Gap,” The wall Street Journal, March 13, 2008, pp. D1, D10). Suppose that the study was based on a sample of 600 men and 700 females, and the standard deviation of the amount spent was $1,200 for men and $1,000 for women. a. State the null and alternative hypothesis if you want to determine whether the mean amount spent is higher for men than for women. b. In the context of this study, what is the meaning of the Type I error? c. In the context of this study, what is the meaning of the Type II error? d. At the 0.01 level of significance, is there evidence that the mean amount spent is higher for men than for women? 10.11 Digital cameras have taken over the majority of the point-and-shoot camera market. One of the important features of a camera is the battery life, as measured by the number of shots taken unit the battery needs to be recharged. The file DigitalCameras contains the battery life of 29 sub-compact cameras and 16 compact cameras (data extracted from “Digital Cameras,” Consumer Reports, July 2009, pp. 28-29). a. Assuming that the population variances from both types of digital cameras are equal is there evidence of a difference in the mean battery life between the two types of digital cameras ()? b. Determine the p-value in (a) and interpret its meaning. c. Assuming that the population variances from both types of digital cameras are equal, construct and interpret a 95% confidence interval estimate of the difference between the population mean battery life of the two types of digital cameras. 10.45 A professor in the accounting department of a business school claims that there is more variability in the final exam scores of students taking the introductory accounting course who are not majoring in accounting than for students taking the course who are majoring in accounting. Random samples of 13 non-accounting majors and 10 accounting majors are selected from the professor’s class roster in his large lecture, and the following results are computed based on the final exam scores: Non-accounting: = 13 = 210.2Accounting: = 10 = 36.5 a. At the 0.05 level of significance, is there evidence to support the professor’s claim? b. Interpret the p-value. c. What assumption do you need to make in (a) about the two populations in order to justify your use of the F test? 10.47 A bank with a branch located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1 pm. lunch period. The waiting time (defined as the time elapsed form when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected (and stored in Bank 1), and the results (in minutes) are as follows: 4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.10 0.38 5.12 6.46 6.19 3.79 Suppose that another branch, located in a residential area, is also concerned with the noon-to-1 pm. lunch period. A random sample of 15 customers is selected (and stored in Bank2), and the results (in minutes) are as follows: 9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35 10.49 6.68 5.64 4.08 6.17 9.91 5.47 a. Is there evidence of a difference in the variability of the waiting time between the two branches? (Use () b. Determine the p-value in (a) and interpret its meaning. c. What assumption about the population distribution of the two banks is necessary in (a)? is the assumption valid for these data? d. Based on the results of (a), is it appropriate to use the pooled-variance t test to compare the means of the two branches?
Answer Below:
Sol x The xxxx and xxxxxxxxxxx hypothesis xx determine xxxxxxx the xxxx amount xxxxx is xxxxxx for xxx than xxx women xxxx hypothesis x m xxx lt x alternative xxxxxxxxxx H x m xxx gt x where x mean xxxxxx spend xx men xxx m xxxx amount xxxxx by xxxxxx Type xxxxx with xxxxxxx to xxx problem xxxxx be xxxxxxxxx the xxxx hypothesis xxxx mean xxxxxx spend xx men xx lower xxxx for xxxxx c xxxx error xxxx context xx the xxxxxxx would xx accepting xxx null xxxxxxxxxx when xxxx amount xxxxx by xxx is xxxxxx than xxx women x We xxxx to xxx the xxxxxxxxx Z x -m xxxxx s x s x Where x m x s x n xxxxxxx all xxx values xx get x based xx significance xxxxx the xxxxxxxx region xxxx between x The xxxxx does xxx lie xxxxxxx the xxxxxxxx region xxxxx we xxxxxx the xxxx hypothesis xxxxxxxxx the xxxx amount xxxxx by xxx is xxxxxx than xxx women xxx a xxxxxx y xxxxxxxxxx TypeSubcompac xxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxx t xxxxxxxxxx COMPACT xxxx m x Variance xxxxxxxx deviation x radic x s x s x n x Where x s x n x Now xxx statistic x m xx s xxxxx n x - x critical xx alpha xxx gt x Therefore xxxxx is xxxxxxxxxxxx evidence xx reject xxx null xxxxxxxxxx b xxx p xxxxx is xxxx means xxxxx is x chance xxxx any xxxxxxxxxx seen xxxx is xxx to xxxxxxxx error x Ho xxxxx sup xx sigma xxx Ha xxxxx sup xxx gt xxxxx sup xxxxxxxxxxx Numerator x f xxxxxxxxxxx d x Critical xxxxx of x Since xxxxxxxxxxx lies xx critical xxxxxx null xxxxxxxxxx is xxxxxxxx Non-accounting xxxxxxxx is xxxxxxx than xxxx of xxxxxxxxxx and xxxxxxxxx claim xx supported xx the xxxxxxxx b xxxxxxx This xxxxx that xx first xxxxxxxx was xxxxxxxx not xxxxxxx than xxx second xxx probability xxxx observed xxxxxxxxx would xxxx occurred xx c xxxxxxxxxx of xxxxxxxxx and xxxxxxxxxxxx of xxxxxxx a xx micro xxxxx Ha xxxxx ne xxxxx Mean xxxx s x t-statistic x sqrt x Degree xx freedom x Critical xxxxxx plusmn xxxxx test xxxxxxxxx lies xx critical xxxxxx null xxxxxxxxxx is xxxxxxxx There xx a xxxxxxxxxx in xxxx waiting xxxxx b xxxxxxx This xxxxx that xx actually xxxxx was xx significant xxxxxxxxxx in xxxxxxx times xxxx the xxxxxxxxxxx that xxx observed xxxxxxxxxx would xxxx occurred xxx c xxx populations xxx normally xxxxxxxxxxx and xxxxxxx are xxxxxxxxxxx and xxxxxx d xxx confidence xxxx d x of xxxxxxxx t xxxxx limit x - xxxx - xxxxx limit x sqrt x So xxxxxxxxxx interval xxx difference xx mean xx -More Articles From Statistics
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