A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random s
ample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample (in years). Assume that the data come from a distribution that is Normally distributed. Complete parts a through c below. Neighborhood 1:
53, 67, 48, 63, 68, 43
Neighborhood 2:
44, 35, 39, 43, 46, 57
(a) Test the null hypothesis at a=0.05 using the pooled t-test. Identify the null and alternative hypotheses.
Compute the t-statistic. Let the difference of the sample means be y1-y2 (round to three decimal places)
Find the P-value. (round to four decimal places as needed)
State the conclusion. Recall that a=0.05.
REJECT or FAIL to REJECT H0. There is SUFFICIENT or INSUFFICIENT evidence to reject the claim that the mean age of houses is the same in the two neighborhoods.
(b) Find a 95% confidence interval using the pooled degrees of freedom.
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(c) A 95% confidence interval for the mean difference in ages of houses in the two neighborhoods was (1.11, 24.89) Is this result different than the result of the pooled t-confidence interval? Explain why or why not. Choose the correct answer below.
- Yes. Since the means are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests.
- Yes. Since the standard deviations are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests.
- No. Since the standard deviations are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests.
- No. Since the means are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests.i
