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An experiment is conducted to compare the starting salaries of male and female college graduates who...

An experiment is conducted to compare the starting salaries of male and female college graduates who find jobs. Pairs are formed by choosing a male and a female with the same major and similar grade point averages. Suppose a random sample of 10 pairs is formed in this manner and the starting annual salary of each person is recorded. The differences within the pairs are obtained by subtracting the female salary from the male salary. The following results are obtained: Mean difference in starting salaries = $400 Standard deviation of the difference in starting salaries = $435 Construct a 95% confidence interval for the true mean difference in starting salaries of the male and female graduates.

Math   Statistics-And-Probability   
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Answer #1

t critical value at 0.05 significance level with 9 df = 2.262

95% confidence interval for d is

d - t * Sd / sqrt(n) < d < d + t * Sd / sqrt(n)

400 - 2.262 * 435 / sqrt(10) < d < 400 + 2.262 * 435 / sqrt(10)

88.84 < d < 711.16

95% CI is ( 88.84 , 711.16) (89 , 711 ) rounded to nearest integer

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