Question

1) A national poll was conducted to determine the proportion of people that prefer a Congressional candidate by the name of Julio. After completing the poll, a 90% confidence interval was calculated to show the proportion of the population that preferred Julio. The confidence interval was:

0.546<p<0.6950.546<p<0.695

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

• Yes
• No

Why or why not?

2) A particular bank requires a credit score of 622 to get approved for a loan. After taking a sample of 176 customers, the bank finds the 95% confidence interval for the mean credit score is:

614< μ <703614< μ <703

Can we be reasonably sure that a majority of people will have a credit score over 622 and be able to get the loan?

• Yes
• No

Why or why not?

Answer 1

1. Yes , we can be reasonably sure that Julio will have at least 50% of the votes .

Reason :

We can see that the 90% confidence interval of the population proportion is from 0.546 to 0.695 or 54.6% to 69.5% . So we are 90% confident that 54.6% to 69.5% people prefer Julio . Which is more than 50% . The whole confidence interval is more than 50% . So we are sure that Julio will have at least 50% of votes.

2. No , we can't be reasonably sure that a majority of people will have a credit score over 622 .

Reason :

The 95% confidence interval of mean credit score is from 614 to 703 . So clearly we can see there is many points in the confidence interval which are less than 622 . The whole confidence intetval is not above 622. So we can't say majority of people will have credit score over 622 .