Question

Question:Chapter 6, Section 4-CI, Exercise 190Use the t-distribution to find a

confidence interval for a difference in means μ1-μ2 given the relevant sample results. Give the best estimate for μ1-μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.

A 95% confidence interval for μ1-μ2 using the sample results x¯1=526, s1=128, n1=400 and x¯2=423, s2=91, n2=200

Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places.

Best estimate = 

Margin of error = 

Confidence interval :  to .

Chapter 6, Section 4-HT, Exercise 210

Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal.

Test H0 : μ1=μ2 vs Ha : μ1≠μ2 using the sample results x¯1=15.3, s1=11.6 with n1=100 and x¯2=18.4, s2=14.3 with n2=80.

(a) Give the test statistic and the p-value.

Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic = 

p-value = 

(b) What is the conclusion of the test? Test at a 10% level.

Reject OR Do Not Reject the HO.

Chapter 6, Section 4-HT, Exercise 216

Is Gender Bias Influenced by Faculty Gender?

In a study¹ examining gender bias, a nationwide sample of 127 science professors evaluated the application materials of an undergraduate student who had ostensibly applied for a laboratory manager position. All the faculty members received the same application, with half randomly given a male name and half randomly given a female name. We see that the applications with female names received a significantly lower recommended salary. Does gender of the evaluator make a difference? In particular, considering only the 64 applications with female names, is the mean recommended salary different depending on the gender of the evaluating faculty member? The 32 male faculty gave a mean starting salary of $27,111 with a standard deviation of $6948 while the 32 female faculty gave a mean starting salary of $25,000 with a standard deviation of $7966.

Let group 1 and group 2 be the salary recommended for female applicants by male faculty members and female faculty members, respectively.

State the null and alternative hypotheses.

Calculate the relevant test statistic.

Round your answer to three decimal places.

t-statistic= 

the absolute tolerance is +/-0.02

Find the p-value.

Round your answer to three decimal places.

p-value = 

the absolute tolerance is +/-0.02

What is the conclusion?

Reject OR Do Not Reject the HO.

Do we have evidence to conclude that mean recommended salary is different depending on the gender of the evaluator?

Yes OR No?

 

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