Question

A random sample of married people were asked “Would you remarry your spouse if you were given the opportunity for a second time?” Of the 150 people surveyed, 127 of them said that they would do so. Find a 95% confidence interval for the proportion of married people who would NOT remarry their spouse. 0.847  0.058 Student A (male) Student score: 448 Mean exa m score: 375 Standard deviation: 32 Student B (female) Student score: 272 Mean exa m score: 247 Standard deviation: 10

A. 0.847  0.058

B. 0.847  0.510

C.0.153 ± 0.0018

D.0.153  0.163

E.0.153  0.058

Answer 1

Solution:

Given,

n = 150 ....... Sample size

Number of people who would remarry their spouse = 127

So ,

Number of people who would NOT remarry their spouse = 150 - 127 = 23

Let denotes the sample proportion of people who would NOT remarry their spouse.

     = x/n   = 23/150 = 0.153  

Our aim is to construct 95% confidence interval for population proportion of people who would NOT remarry their spouse.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96

Now , the margin of error is given by

E = /2 *

= 1.96 * [0.153 *(1 - 0.153  )/150]

= 0.058

Now , confidence interval is given by

   E

0.153   0.058