Question

Suppose that we wish to assess whether more than 60 percent of all U.S. households in a particular income class bought life insurance last year. That is, we wish to assess whether p, the proportion of all U.S. households in the income class that bought life insurance last year, exceeds .60. Assume that an insurance survey is based on 1,000 randomly selected U.S. households in the income class and that 640 of these households bought life insurance last year.

a)   Assuming that p equals .60 and the sample size is 1,000, what is the probability of observing a sample proportion that is at least .64?

b)  Based on your answer in part a, do you think more than 60 percent of all U.S. households in the income class bought life insurance last year? Explain.

Answer 1

Answer:

Given that:

Suppose that we wish to assess whether more than 60 percent of all U.S. households in a particular income class bought life insurance last year. That is, we wish to assess whether p, the proportion of all U.S. households in the income class that bought life insurance last year, exceeds .60.

Assume that an insurance survey is based on 1,000 randomly selected U.S. households in the income class and that 640 of these households bought life insurance last year.

a) Assuming that p equals .60 and the sample size is 1,000, what is the probability of observing a sample proportion that is at least .64?

Find the probability of observing a sample proportion that is at least 0.64

The test hypothesis are given below

Null hypothesis

Alternative hypothesis:

Compute

Find

Use P-value calculator, the probability value of two tailed z is 0.0099

Therefore

Thus, the probability of observing a sample proportion that is at least 0.64 is 0.0049

b) Based on your answer in part a, do you think more than 60 percent of all U.S. households in the income class bought life insurance last year? Explain.

Yes, more than 60% of all U.S. households in the income class bought life insurance last year.

Explanation:

Use the level of significance, =0.05.

From part (a), the value of p is 0.0049.

Here, the value of p is lesser than the level of significance.

That is  

Thus, reject the null hypothesis

Hence, it can be concluded that more than 60% of all U.S. household in the income class bought life insurance last year.