Question

PLEASE SHOW WORK. It is necessary to round a probability to 2 decimal places. I must understand so clear writing is much appreciated.

All test of hypotheses are to be done at the 5% level of significance and all confidence intervals are to be 95% unless otherwise stated.

1. According to statistics report, a surprising number of motor vehicles are not covered by insurance. Sample results from a poll showed that 52 of 200 vehicles (0.26 or 26%) were not covered by insurance.

a. Make a 95% confidence interval for the percentage of motor vehicles that are not insured.

b. If some vehicle company claimed that the national proportion of motor vehicles that are not covered by insurance is 30%, is this claim reasonable? Why?

c. What is the maximum 95% margin of error for the percentage of motor vehicles that are not insured?

Answer 1

a) The estimated proportion is . Sample size is .

The confidence interval for proportion is

The 95% two-sided confidence interval for proportion is

b)We have to test

The test statistic is

The P-value of the test is

Since the P-value is , we accept the null hypothesis. Strong evidence to support Null hypothesis.

We are 95% confident that the claim is reasonable.

c)The maximum margin of error for a particular sample size is obtained when p = 0.5 (equivalent to 50%).

The maximum margin of error is