Question

Number of Sample Mean Salary Sample Standard Deviation Professors (in 1000s) (in $1000) English 32 71.4 10.7 Statistics 35 76.3 13 A. Are the assumptions for constructing a confidence interval for the difference between two population means satisfied in this case? No, the assumptions for the assumptions for constructing a confidence interval for the difference between two population means are not satisfied because the sample sizes are not large enough. No, the assumptions for constructing a confidence interval for the difference between two population means are not satisfied because we were not told that both samples come from normal distribution. Yes, the assumptions for constructing a confidence interval for the difference between two population means are satisfied because both sample sizes are large enough. Yes, the assumptions for the assumptions for constructing a confidence interval for the difference between two population means are satisfied because annual salaries are always normally distributed regardless of the sample size. B. Construct and interpret a 95% confidence interval for the difference between mean salaries of English and Statistics professors. Let 1 = English professors, 2 = Statistics professors. 95% CI for $\mu_1 - \mu_2$: Round to 4 decimal places. C. Interpret the interval you constructed in part B.

          Number of Sample Mean Salary Sample Standard Deviation
Professors
(in 1000s)
(in $1000)
English 32
71.4
10.7
Statistics 35
76.3
13
A. Are the assumptions for constructing a confidence interval for the difference between two population means satisfied in this case?
No, the assumptions for the assumptions for constructing a confidence interval for the difference between two population means are not
satisfied because the sample sizes are not large enough.
No, the assumptions for constructing a confidence interval for the difference between two population means are not satisfied because
we were not told that both samples come from normal distribution.
Yes, the assumptions for constructing a confidence interval for the difference between two population means are satisfied because both
sample sizes are large enough.
Yes, the assumptions for the assumptions for constructing a confidence interval for the difference between two population means are
satisfied because annual salaries are always normally distributed regardless of the sample size.
B. Construct and interpret a 95% confidence interval for the difference between mean salaries of English and Statistics professors. Let 1 =
English professors, 2 = Statistics professors.
95% CI for $\mu_1 - \mu_2$:
Round to 4 decimal places.
C. Interpret the interval you constructed in part B.

$Number of Sample Mean Salary Sample Standard Deviation Professors (in 1000s) (in 1000) English 32 71.4 10.7 Statistics 35 76.3 13 A. Are the assumptions for constructing a confidence interval for the difference between two population means satisfied in this case? No, the assumptions for the assumptions for constructing a confidence interval for the difference between two population means are not satisfied because the sample sizes are not large enough. No, the assumptions for constructing a confidence interval for the difference between two population means are not satisfied because we were not told that both samples come from normal distribution. Yes, the assumptions for constructing a confidence interval for the difference between two population means are satisfied because both sample sizes are large enough. Yes, the assumptions for the assumptions for constructing a confidence interval for the difference between two population means are satisfied because annual salaries are always normally distributed regardless of the sample size. B. Construct and interpret a 95% confidence interval for the difference between mean salaries of English and Statistics professors. Let 1 = English professors, 2 = Statistics professors. 95% CI for $\mu1 - \mu2$: Round to 4 decimal places. C. Interpret the interval you constructed in part B.$

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