Question

1-) Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it uses different media to reach potential buyers. The mean annual family income for 12 people making inquiries at the first development is $153,000, with a standard deviation of $42,000. A corresponding sample of 24 people at the second development had a mean of $171,000, with a standard deviation of $30,000. Assume the population standard deviations are the same. At the 0.05 significance level, can Fairfield conclude that the population means are different?

1. State the decision rule for 0.05 significance level: H₀: μ₁ = μ₂; H₁:μ₁ ≠ μ₂. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Reject H0 if t is not between ____________ and _____________.

b.Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Value of the test statistic ____________

c. At the 0.05 significance level, can Fairfield conclude that the population means are different?

__________ (reject/ do not reject) Ho. Fairfield __________ (can/cannot) conclude that the population means are different.

Answer 1

Given that,

For 1st development : n1=12, x1-bar = $153000 and s1 = $42000

For 2nd development : n2=24, x2-bar = $171000 and s2 = $30000

Assume the population standard deviations are the same, so we used the pooled variance.

Pooled variance is,

a) The null and alternative hypotheses are,

H0 : μ1 = μ2

H1 : μ1 ≠ μ2

This hypothesis test is a two-tailed test.

Degrees of freedom = 12 + 24 - 2 = 34

Using t-table we get, t-critical values at significance level of 0.05 with 34 degrees of freedom are, tcrit = ± 2.032

Decision Rule : Reject H0 if t is not between -2.032 and 2.032

b) Test statistic is,

The value of the test statistic is -1.482

c) Since, test statistic = -1.482 is between -2.032 and 2.032, we do not reject H0. Fairfield cannot conclude that the population means are different.