Question

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:

	Too Small	Too Large	Total
Low Income	18	22	40
High Income	19	16	35
Total	37	38	75

For children in the low income group, find a 90% confidence interval for the proportion of children that drew the nickel too large.

Give all answers correct to 3 decimal places.

a) Critical value (positive value only): Correct

b) Margin of error: .129Correct  

c) Confidence interval: .421 < pp < .679 ? not sure if this is correct?

d) Does the confidence interval support the claim that more than 40% of children from the low income group draw nickels too large?

• Confidence interval supports claim
• Confidence interval does not support claim

Answer 1

n = 40, x = 22

p̂ = x/n = 0.55  

a) At α = 0.1, two tailed critical value, z_c = NORM.S.INV(0.1/2) = 1.645

b) Margin of error, E = z*√(p̂ *(1- p̂)/n) =1.645 *√(0.55*0.45/40) = 0.129

c) 90% Confidence interval :  

Lower Bound = p̄ - E = 0.55 - 0.129 =    0.421

Upper Bound = p̄ + E = 0.55 + 0.129 =    0.679

0.421 < p < 0.679  

d) As the confidence interval do not contain 0.40 and both the values are greater than 0.40 so we can reject the null hypothesis.

Confidence interval supports claim.