Question

A survey of 725 teenagers between the ages of 13 and 18 conducted by JA Worldwide/Deloitte &

Touche USA LLP found that 69% agree that people who practice good business ethics are more

successful than those who do not (source: “2007 Executive Summary: JA Worldwide/Deloitte Teen

Ethics Survey”).

a. Calculate the 90% confidence interval estimate for the true population proportion, p, given the survey

information.

b. What is the largest possible sample size needed to estimate the true population proportion, p, within

a margin of error of 0.02 with a confidence level of 95% if there was no prior knowledge concerning

the proportion of respondents who would agree with the survey’s question?

c. If the survey in part a had a margin of error of 0.04 percentage points, determine the level of

confidence that was used in estimating the population proportion if there was no prior knowledge

concerning the percentage of teenagers who would respond as they did.

d. A survey conducted at a Midwestern university and involving 1,500 students found that 68% had

taken out a student loan to help pay for the cost of their college education. A similar study at a

southeastern university in which 2,000 students were surveyed found that 47% had taken out a student

loan.(1.) Develop and interpret a 95% confidence interval estimate for the difference in the proportions of

students who have loans at these two universities.(2.)Using an alpha level of 0.05, test the hypothesis that there is no difference in the proportions of

students at these two universities who have loans. How does this test compare with the result you found

in part a?

e. The consistency of the diameters of wheel bearings is vital to the operation of the wheel. The

specifications require that the variance of these diameters be no more than 0.0015 centimeter squared.

The diameter is continually monitored by the quality-control team. Twenty subsamples of size 10 are

obtained every day. One of these subsamples produced bearings that had a variance of 0.00317

centimeter squared.

Conduct a hypothesis test to determine if the quality control team should advise management to stop

production and search for causes of the inconsistency of the bearing diameters. Use a significance level

of 0.05. (Use p-value approach!)

Answer 1

(a)

Sample proportion is

For 90% confidence interval, using excel function "=NORMSINV(0.95)", critical value of z will be
---------------------------

Confidence interval for population proportion will be

(b)

Since no estimate of popualiton poportion is given so let

The critical value of z for 95% confidence interval is .

The margin of error E= 0.02, so required sample size will be

?

So required sample size for 95% confidence interval is 2401.

(c)

Since no estimate of popualiton poportion is given so let

The critical value of z for 95% confidence interval is .

The margin of error E= 0.04, so required sample size will be

So required sample size for 95% confidence interval is 601.