Question

Software analysis of the salaries of a random sample of 251 teachers in a particular state produced the confidence interval shown below. Determine if the following conclusions are correct. If​ not, state what is wrong with the conclusion. Complete parts a through e below. ​t-interval for mu ​: with 99 ​% ​confidence, 43623 less thanmu​(TchPay)less than45465 ​

a) If many random samples of 251 teachers from this state were​ taken, about 99 out of 100 of them would produce this confidence interval. Choose the correct answer below.

A. This conclusion is​ correct, assuming all assumptions and conditions are met.

B. This conclusion is incorrect. About 99 out of 100 intervals will produce a confidence interval that overlaps with this interval.

C. This conclusion is incorrect. About 99 out of 100 intervals based on samples of any size would produce this confidence interval.

D. This conclusion is incorrect. About 99 out of 100 intervals will contain the true mean​ salary, but different samples of 251 teachers will produce different confidence intervals. ​

b) If many random samples of teachers from this state were​ taken, about 99 out of 100 of them would produce a confidence interval that contained the mean salary of all teachers from this state. Choose the correct answer below.

A. This conclusion is​ correct, assuming all assumptions and conditions are met.

B. This conclusion is incorrect. All 100 of the intervals will contain the true mean​ salary, but different samples of 251 teachers will produce different confidence intervals.

C. This conclusion is incorrect. About 99 out of 100 teachers surveyed will earn a salary within the interval.

D. This conclusion is incorrect. About 99 out of 100 intervals will produce a confidence interval that overlaps with this interval. ​

c) About 99 out of 100 teachers from this state earn between ​$43 comma 623 and ​$45 comma 465 . Choose the correct answer below.

A. This conclusion is incorrect. The interval is for the population mean​ salary, not the salary for individual teachers.

B. This conclusion is​ correct, assuming all assumptions and conditions are met.

C. This conclusion is incorrect. The interval means that a newly hired teacher in this state has a 99 ​% chance of earning between ​$43 comma 623 and ​$45 comma 465 .

D. This conclusion is incorrect. The interval is for the sample mean​ salary, not the salary for individual teachers. ​

d) About 99 out of 100 of the teachers surveyed earn between ​$43 comma 623 and ​$45 comma 465 . Choose the correct answer below.

A. This conclusion is incorrect. The interval is for the population mean​ salary, not the salary for individual teachers.

B. This conclusion is​ correct, assuming all assumptions and conditions are met.

C. This conclusion is incorrect. The interval is for the sample mean​ salary, not the salary for individual teachers.

D. This conclusion is incorrect. The interval means that a newly hired teacher in this state has a 99 ​% chance to earn between ​$43 comma 623 and ​$45 comma 465 . ​

e) We are 99 ​% confident that the average teacher salary in the entire country is between ​$43 comma 623 and ​$45 comma 465 . Choose the correct answer below.

A. This conclusion is incorrect. The confidence interval addresses only the salaries of teachers in this state.

B. This conclusion is​ correct, assuming all assumptions and conditions are met.

C. This conclusion is incorrect. The confidence interval addresses only the salaries of teachers surveyed in the sample of 251 .

D. This conclusion is incorrect. A larger sample from the state is needed in order to construct a confidence interval estimate for the salaries of teachers across the entire country.

Answer 1