Question

PART 3 - Create a confidence interval for a proportion.
Investigate the proportion of married patients.

3a. Write a reason why you would want to estimate this population proportion. What can be learned?

3b. State the sample size, n, and the sample proportion, "p bar" (p with a line over it).

3c. Calculate a 95% confidence interval for the population proportion, p. Report at least four decimal places.

Marital Status

M

S

DWS

M

M

M

DWS

M

M

S

S

S

DWS

S

DWS

S

M

M

M

M

M

M

DWS

S

S

M

S

S

DWS

S

M

DWS

DWS

S

M

S

S

S

S

M

DWS

M

M

S

S

M

DWS

S

S

DWS

S

S

S

M

M

DWS

S

M

M

DWS

M

M

S

M

M

M

S

M

S

M

M

DWS

S

S

DWS

S

M

S

M

S

M

M

M

DWS

M

S

S

M

S

S

S

M

*M = Married.

*S = Single.

*DWS = Divorced, Widowed, or Separated

Answer 1

The number of data given here is 92.

So n=92

Number of success in the sample is equal to the number of married people in the sample (x).

So x=39

To find confidence interval we should find and

= x/n= 39/92= 0.423 which is the sample proportion.

=1-= 1- 0.423=0.576

Confidence Interval given= 0.95

= 1- CL= 1-0.95=0.05

=   

= 1.96

This value can be found from standard probability distribution table.

We estimate with 95% confidence that 32.21% to 52.38% of people are married.

95% of confidence level constructed in this way would contain true value of the population proportion of people who are married.