Question

1. Use the following information for the next four problems.  Suppose that a researcher is interested in estimating , the proportion of all people in a particular area with diabetes.

   Suppose the researcher selects a random sample of 500 people and finds 47 of them to have diabetes. Calculate a 95% confidence interval to estimate the proportion of all people in the area with diabetes.

   	a.	0.094  0.012
   	b.	0.094  0.083
   	c.	0.094  0.026
   	d.	0.094  0.021

QUESTION 7

1. Refer back to the story and to the confidence interval in Problem 6. Select the pair of words below that best completes the following two statements.

   (i) A 99% confident interval (based on the original sample of 500 people) would be __________ than the confidence interval in Problem 6.

   (ii) A 95% confident interval based on a larger sample (assuming that the value of  doesn’t change) would be __________ than the confidence interval in Problem 6.

   	a.	(i) shorter     (ii) longer
   	b.	(i) longer     (ii) longer
   	c.	(i) shorter   (ii) shorter
   	d.	(i) longer     (ii) shorter

QUESTION 8

1. For the next two problems only, suppose that the confidence interval in Problem 6 had ranged from 0.074 to 0.114.

   Which one of the following would give a correct interpretation?

   	a.	We are confident that 95% of the people in the area have diabetes.
   	b.	We are 95% confident that , the population percent, is between 0.074 and 0.114.
   	c.	We are 95% confident that exactly 47 people have diabetes.
   	d.	We are 95% confident that , the sample percent, is between 0.074 and 0.114.

QUESTION 9

1. Suppose someone makes the claim that 8% of the people in the area have diabetes. Should we believe the claim? Why or why not?

   	a.	We should believe the claim because 8% is in the confidence interval.
   	b.	We should believe the claim because 8% is not in the confidence interval.
   	c.	We should not believe the claim because 8% is not in the confidence interval.
   	d.	We should not believe the claim because 8% is in the confidence interval.

Answer 1

We need to construct the 95% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	47
Sample Size N =	500

The critical value for α=0.05 is z_c = 1.96. The corresponding confidence interval is computed as shown below:

c.	0.094  0.026

QUESTION 7

(i) A 99% confident interval (based on the original sample of 500 people) would be longer than the confidence interval in Problem 6.

As the significance level increases the confidence interval increases.

(ii) A 95% confident interval based on a larger sample (assuming that the value of  doesn’t change) would be shorter than the confidence interval in Problem 6.

As the sample size increases the confidence interval decreases.

d) (i) longer     (ii) shorter

QUESTION 8

b) We are 95% confident that , the population percent, is between 0.074 and 0.114.

As the confidence interval estimate about the population

QUESTION 9

a) We should believe the claim because 8% is in the confidence interval.