Question

8. The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 60 Houston residents the mean is 25.5 miles a day and the standard deviation is 7.9 miles a day, and for an independent simple random sample of 35 Seattle residents the mean is 21.1 miles a day and the standard deviation is 8.9 miles a day. Formulate a hypothesis to test whether the difference in the mean distance travel per day is the same between Houston and Seattle. That is, test the following null hypothesis at the 5% significance level: vs. the 2-sided alternative Note: Compared to Hypo Testing for one sample mean, Hypothesis testing for the difference of of two sample means uses different formulas to find the test-statistic and the degree of freedom. You do not need to know those formulas. • Based on those formula, for this problem, the test-statistic is: 2.42 • To find the critical value, find the critical value from the t- distribution table that corresponds to degree of freedom 65 (the approximate degree of freedom in this case) and the significance level here (2-sided test)

Answer 1

Answer:

Int: H = Ty!: 'H

Calculated t=2.42

Given Df = 65

Critical value of t with 65 DF at 0.05 level = 1.997

Rejection Region: Reject Ho if t < -1.997 or t > 1.997

Calculated t = 2.42 falls in the rejection region

The null hypothesis is rejected.

There is sufficient evidence to conclude that there is significant difference in the mean distance travel per day between Houston and Seattle.

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	60
Sample Mean	25.5
Sample Standard Deviation	7.9000
Population 2 Sample
Sample Size	35
Sample Mean	21.1
Sample Standard Deviation	8.9000
Intermediate Calculations
Numerator of Degrees of Freedom	10.9119
Denominator of Degrees of Freedom	0.1690
Total Degrees of Freedom	64.5749
Degrees of Freedom	64
Standard Error	1.8175
Difference in Sample Means	4.4000
Separate-Variance t Test Statistic	2.4209
Two-Tail Test
Lower Critical Value	-1.9977
Upper Critical Value	1.9977
p-Value	0.0183
Reject the null hypothesis