Question

Arbitron Media Research Inc. conducted a study of the iPod listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for a sample of 13 men was 30 minutes per day. The standard deviation was 13 minutes per day. The mean listening time for a sample of 11 women was also 30 minutes, but the standard deviation of the sample was 14 minutes. Use a two-tailed test and at 0.02 significance level, can we conclude that there is a difference in the variation in the listening times for men and women? (Round your answer to 3 decimal places.) The test statistic is . Decision: H0:σ21=σ22.

Answer 1

Solution For men number of samples = 13. mean time = 30 standard deviation = 13 minutes minutes. for women number of samples = 11 mean time to =30 standard deviation - 14 minutes = 12 Let ²= variation in the listening time for men (2 = variation in the listening time to women. Given na 13 8 = 13² = 169 s² = 14² = 196 t na =)) 82 > 8.2 23 is in the numerater 8 is in denominater in in f-statistics and f statistics. hypothesis are Hoi 5² = 82² US Hi: 8² & 82² (Two tall)

Date Page: Test statistics is Feat = 122 132 = 196 169 Feat= 51.159 ftable = - fm-l, n2-18 12 Ful- 13,1. 0.02 - Flo, 12,0.01 Frable 2.4.29 . Observed in a statistical table for at f we reject Ho at al. los if - Fral > Foll, 02-1812 Here 1.159 $ 4.292 10 le 1.159 (4.29 we fail to reject Ho: 0,² = 52 at 0.02 significant level.. conclusion - variation and women are in the listening same. timen for men