Question

a.

A national poll was conducted to determine the proportion of people that prefer a Congressional candidate by the name of Krystal. After completing the poll, a 95% confidence interval was calculated to show the proportion of the population that preferred Krystal. The confidence interval was:

0.478<p<0.5740.478<p<0.574

Can we be reasonably sure that Krystal will have at least 50% of the vote?

b.

A particular bank requires a credit score of 604 to get approved for a loan. After taking a sample of 144 customers, the bank finds the 95% confidence interval for the mean credit score is:

625< μ <725625< μ <725

Can we be reasonably sure that a majority of people will have a credit score over 604 and be able to get the loan?

Answer 1

a) As 0.5 lies inside the confidence interval here, therefore the test is not significant here. Therefore we dont have sufficient evidence here that  Krystal will have at least 50% of the vote.

The test would have been significant if the whole confidence interval for the proportion who vote Krystal would have lied above 0.5.

b) As the whole 95% confidence interval for the population mean credit score lies above 604, that is the lower limit of the confidence interval that is 625 is greater than 604, therefore we have sufficient evidence here that a majority of people will have a credit score over 604 and be able to get the loan.