Question

A random sample of 125 adults was given an IQ test. It was found that 60 of them scored higher than 100. Based on this, compute a 95% confidence interval for the proportion of all adults whose IQ score is greater than 100. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval?

Answer 1

Solution :

Given that,

n = 125

x = 60

Point estimate = sample proportion = = x / n = 0.48

1 - = 0.52

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.48 * 0.52 ) / 125)

= 0.088

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.48 - 0.088 < p < 0.48 + 0.088

0.39 < p < 0.57

The lower limit of the 95% confidence interval is 0.39.

The upper limit of the 95% confidence interval is 0.57.