Question

Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set α =  0.10. The critical value for this hypothesis test would be ________.

		1.645
		1.28
		2.33
		1.96

Answer 1

The data is given as follows: Population Sample mean Sample size Population standard deviation q=3.9 Play Station user Xbox user = 34.2 T = 32.7 n = 36 n = 30 0 =4.0 Let 14 denotes the population mean of Play station user. Let U2 denotes the population mean of Xbox user. The hypothesis is given as follows: The null hypothesis is H, : the mean of the Play station user is the same as the mean of Xbox user. The alternative hypothesis is H : the mean of the Play station user is different from the mean of Xbox user. Mathematically, it is written as follows: The null hypothesis is H:44 = the The alternative hypothesis is H.:47 12. This is a two-tailed test. As the population standard deviation is given, then Z-test will be used. The level of significance is a=0.10. The critical value of Z-statistic at 10% level of significance for the two-tailed test is 20.12 = +1.645 Hence, the critical value for this hypothesis test is 1.645.

Answer 2

Solution: Given Data Play station users: Sample mean (3) 34,2 Sample size (n.) = 36 standard deviation (-)- 3.9 Xbox users. Sample mean ( 32) = 32.7 Sample Sizelną) = 30 standard deviation (+2) - 4.0 null hypothesis (Ho): H1 M2 Alternative hypothesis CMa): M.#Mz so this is two tailed test signibicance level(a) = 0,10

G The exilical value of a.slatistic at 10% level of Signibicane bor the two. tailed test is d: 0.10 /= 0.10 7 2/2 Zo.10 70.05 = +1.645 (": from 2 table) 70.05 1,645 the critical value for this hypothesis test is [1.645 So is currect answer the first option (1.645