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. If Population 1 is defined as PlayStation users and Population 2 is defined as Xbox users, the correct hypothesis statement for this hypothesis test would be

		H0: μ1 - μ2 ≤ 0; H1: μ1 - μ2 > 0
		H0: μ1 - μ2 = 0; H1: μ1 - μ2 ≠ 0
		H0: μ1 - μ2 ≥ 0; H1: μ1 - μ2 < 0
		H0: μ1 - μ2 ≠ 0; H1: μ1 - μ2 = 0

Answer 1

To Test -

H₀: μ₁ - μ₂ = 0; H₁: μ₁ - μ₂ ≠ 0

Test Statistic :-

Z = (X1 – X2)/ (o/nl) + (ož/n2)

$Z = ( 34.2 - 32.7 ) / \sqrt{( 3.9^{2} /36 ) + ( 4^{2}/30 )}$
Z = 1.5343

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2)
Critical value Z(α/2) = Z(0.1 /2) = 1.645
| Z | > Z(α/2) = 1.5343 < 1.645
Result :- Fail to Reject Null Hypothesis