Question

Suspecting that television repair shops tend to charge women more than they do men, Emily disconnected the speaker wire on her portable television and took it to a sample of 12 shops. She was given repair estimates that averaged $85, with a standard deviation of $28. Her friend John, taking the same set to another sample of 9 shops, was provided with an average estimate of $65, with a standard deviation of $21. Assuming normal populations with equal standard deviations, use the 0.05 level in evaluating Emily’s suspicion

Answer 1

H₀:

H₁:

The pooled variance(s_p²) = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2)

                                         = (11 * (28)^2 + 8 * (21)^2)/(12 + 9 - 2)

                                         = 639.6

The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

                             = (85 - 65)/sqrt(639.6/12 + 639.6/9)

                             = 1.79

DF = 12 + 9 - 2 = 19

At alpha = 0.05, the critical value is t^* = 1.729

Since the test statistic value is greater than the critical value (1.79 > 1.729), so we should reject the null hypothesis.

So at 0.05 significance level, there is sufficient evidence to support Emily's suspicion that television repair shops tend to charge women more than they do men.