Question

A random sample of 250 men yielded 175 who said they'd ridden a motorcycle at some time in their lives, while a similar sample of 215 women yielded only 43 that had done so. Find a 99% confidence interval for the difference between the proportions of men and women who have ridden motorcycles.
a. .5 ± .103

b. .5 ± .085

c. .5 ± .112

d. .4688 ± .085

e. .5 ± .078

Answer 1

Answer:

Option a is right

Step-by-step explanation:

Given that a random sample of 250 men yielded 175 who said they'd ridden a motorcycle at some time in their lives, while a similar sample of 215 women yielded only 43 that had done so.

For proportions since binomial and sample size large we can use  z critical values.

Sample             I            II

N                    250        215     465

X                     175           43    218

p                       0.7          0.2    0.4688

p difference = 0.5

Std error of difference = $\sqrt{p(1-p)(\frac{1}{n_1}+ \frac{1}{n_2} }\\=\sqrt{0.4688*0.5312)(\frac{1}{250} + \frac{1}{215} )}\\=0.0409$

Margin of error for 99% = 2.58*std error =  0.105

Confidence interval 99% = (0.5±0.105)            

Option a is right.