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

.

Answer 1

ANSWER:

Software analysis of the salaries of a random sample of 251:

Required information is given by ,

99 % confidence interval = 43,623 < mu < 45,465.

CALCULATED:

a) If many random samples of 251 teachers from this state were​taken:

We have to obtained the correct statement this ccnfidence interval is

Here,

We observed the the given confidence interval then this stati=ement is  the 99 out of 100 intervals will contain the true mean​ salary, but different samples of 251 teachers will produce different confidence intervals. ​

Therefore,

OPTION (D) is correct answer.

b) If many random samples of teachers from this state were​taken, about 99 :

We have to obtained the correct statement this ccnfidence interval is,

Here,

We observed the given confidence interval is assuming all assumptions and conditions are met.

Therefore ,

OPTION (A) is correct answer.

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

​(c) About 99 out of 100 teachers from this state earn between​$43 :

We have to obtained the correct statement this ccnfidence interval is,

Here,

• The interval is for the population mean​ salary, not the salary for individual teachers.