Question

A sample of 30 randomly selected student cars have ages with a mean of 7.3 years and a standard deviation of 3.6 years, while a sample of 19 randomly selected faculty cars have ages with a mean of 5 years and a standard deviation of 3.7 years.

1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars.

(a) The test statistic is ???

(b) The critical value is ???

(c) Is there sufficient evidence to support the claim that student cars are older than faculty cars?

A. No

B. Yes

2. Construct a 99% confidence interval estimate of the difference μs−μf, where μs is the mean age of student cars and μf is the mean age of faculty cars.

???<(μs−μf)<???

Answer 1

The test hypothesis is


This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

a) Now, the value of test static can be found out by following formula:


b) Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 30 + 19 - 2 = 47
This implies that

c) Since, we fail to reject the null hypothesis . A. NO

2. Confidence interval(in %) = 99

Since we know that

Required confidence interval = (2.3-2.8645, 2.3+2.8645)

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