Question

Using the data in the worksheet Consumer Transportation Survey, develop 95% confidence intervals for the following:

a. the proportion of individuals who are satisfied with their vehicle

b. the proportion of individuals who have at least one child

Satisfaction with vehicle	Number of Children
Yes	0
Yes	1
No	0
No	0
Yes	0
Yes	2
Yes	3
Yes	2
Yes	0
Yes	2
Yes	1
Yes	4
No	1
Yes	0
Yes	0
Yes	0
No	1
No	1
Yes	1
Yes	0
No	2
Yes	1
Yes	4
Yes	1
No	2
Yes	2
Yes	4
Yes	3
Yes	0
No	0
Yes	0
Yes	0
No	0
Yes	0
Yes	0
No	0
No	2
No	2
Yes	2
No	1
Yes	1
Yes	1
Yes	1
Yes	1
Yes	0
Yes	0
Yes	0
No	0
Yes	0
No	0

Answer 1

a)

Total Number of people, n = 50

Number of people satisfied with their vehicle, x = 35

p̅ = x/n = 0.7

95% Confidence interval for the proportion of individuals who are satisfied with their vehicle:

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.960

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.7 - 1.96 *√(0.7*0.3/50) = 0.5730

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.7 + 1.96 *√(0.7*0.3/50) = 0.8270

0.573 < p < 0.827

b)

Total Number of people, n = 50

Number of people who have at least one child, x = 27

p̄ = x/n = 0.54

95% Confidence interval for the proportion of individuals who have at least one child:

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.960

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.54 - 1.96 *√(0.54*0.46/50) = 0.4019

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.54 + 1.96 *√(0.54*0.46/50) = 0.6781

0.4019 < p < 0.6781