Question:Chapter 6, Section 4-CI, Exercise 190

Use thet-distribution to find a confidence interval for a difference in means1-2given the relevant sample results. Give the best estimate for1-2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.

A95%confidence interval for1-2using the sample resultsx1=526,s1=128,n1=400andx2=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 thet-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.

TestH0:1=2vsHa:12using the sample resultsx1=15.3,s1=11.6withn1=100andx2=18.4,s2=14.3withn2=80.

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

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

test statistic=

p-value=

(b) What is the conclusion of the test? Test at a10%level.

Reject OR Do Not Reject the HO.

Chapter 6, Section 4-HT, Exercise 216

Is Gender Bias Influenced by Faculty Gender?

In a study¹examining gender bias, a nationwide sample of127science 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 the64applications with female names, is the mean recommended salary different depending on the gender of the evaluating faculty member? The32male faculty gave a mean starting salary of$27,111with a standard deviation of$6948while the32female faculty gave a mean starting salary of$25,000 with a standard deviation of$7966.

Let group1and group2be 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 thep-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?