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

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

3. 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 95% confident that , the population percent, is between 0.074 and 0.114.
   	b.	We are confident that 95% of the people in the area have diabetes.
   	c.	We are 95% confident that , the sample percent, is between 0.074 and 0.114.
   	d.	We are 95% confident that exactly 47 people have diabetes.

4. 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 in the confidence interval.
   	d.	We should not believe the claim because 8% is not in the confidence interval.

5. Drivers in the United States are keeping their cars longer. To plan production and sales events, a company wants to estimate the proportion of automobiles that are more than ten years old and still on the road. The company wants to be 95% confident that their sample estimate is accurate to within 4% of the actual population proportion. How large of a sample should the company select? (Assume that there is no prior information regarding the true value of the population proportion. Hint – that means to let  = 0.50.)

   	a.	4
   	b.	142
   	c.	13
   	d.	601

Answer 1

1)

sample success x =		47
sample size          n=		500
sample proportion p̂ =x/n=		0.0940
std error se= √(p*(1-p)/n) =		0.0131
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0256

option C is correct : 0.094 -/+ 0.026

2)option B is correct

(i) longer     (ii) shorter

3)

option A

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

4)

option A

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

5)

here margin of error E =	0.04
for95% CI crtiical Z          =	1.960
estimated prop.=p=	0.5000
reqd. sample size n=	p*(1-p)*(z/E)2=	601