Question

1. A company contemplating the introduction of a new product wants to estimate the percentage of the market that this new product might capture. In a survey, random samples of 100 customers were asked whether or not they would purchase this new product. Fourteen responded affirmatively. The 90% confidence interval for the population proportion of potential customers that would purchase the new product is (0.08, 0.20).

a) Does the sample proportion lie in the interval (0.08, 0.20)? Yes/No?

b) Based on the scenario from the above question. Does the population proportion lie in the interval (0.08, 0.20)? Yes/No?

c) If we use a 95% confidence level instead of a 90% confidence level, will the confidence interval calculation from the same data produce an interval narrower than (0.08, 0.20)? Yes/No?

Answer 1

a) Does the sample proportion lie in the interval (0.08, 0.20)? Yes/No?

Yes, because the point estimate for the confidence interval of proportion is the sample proportion, which is 0.14 this can be also calculated as:

(0.08+0.20)/2..

=>0.14 and also given that out of 100, 14 have affirmatively replied so, the sample proportion is 0.14.

b) Based on the scenario from the above question. Does the population proportion lie in the interval (0.08, 0.20)? Yes/No?

Yes at a 90% confidence level we can say that the population proportion does lie in the calculated confidence interval.

c) If we use a 95% confidence level instead of a 90% confidence level, will the confidence interval calculation from the same data produce an interval narrower than (0.08, 0.20)? Yes/No?

No, If we use a confidence interval of 95% rather than 90% then the confidence interval will be wider than that of 90% because the Zc value will be larger for 95% confidence level which will increase the margin of error value hence widening the confidence interval.