Question

Round to the fourth and write as a proportion unless otherwise stated.

Problem 3

A sociologist randomly sampled 200 people who worked in computer-related jobs and found that 21%
of them have changed jobs over the last six months.
a. For a 99% confidence interval, find the margin of error for the true proportion that changed their jobs over the last six months.
b. Build and interpret a 99% confidence interval for the proportion that changed their jobs over the last six months.
c. Respond to the claim that more than 12% have changed their job in the last six months. Make your response understandable to someone not in the class. d. Respond to the claim that less than 27% have changed their job in the last six months. Make your response understandable to someone not in the class.

Conduct a full hypothesis test for the following. Be sure to state your hypothesis, verify or assume
requirements, state your test statistic, state the p-value, state your decision rule and conclusion.

Answer 1

The confidence interval for proportion is

a) For a 99% confidence interval, , the margin of error for the true proportion is

b) The 99% Confidence interval is

c)We have to test (right tailed Z-test)

The test statistic is

The P-value of the test is

Since , we reject the null hypothesis.

Conclusion: "with 99% confidence, more than 12% have changed their job in the last six months".

d)We have to test (left tailed Z-test)

The test statistic is

The P-value of the test is

Since , we accept the null hypothesis.

Conclusion: "with 99% confidence, we cannot say that less than 27% have changed their job in the last six months".