Question

1. According to data from Ipsos Global Express, 64% of Americans say there is never enough time in the day to get thins done. Suppose this percentage is based on a random sample of 900 Americans.

1. Find a 90% confidence interval for the corresponding population proportion.

________________

2. What is the margin of error for this estimate?   ____________

Answer 1

Solution :

(a)Given that,

n = 900

Point estimate = sample proportion = = 0.64

1 - = 1-064=0.36

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 (((0.64*0.36) / 900)

= 0.026

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.64-0.026 < p < 0.64+0.026

0.614< p <0.666

The 90% confidence interval for the population proportion p is :(0.614 ,0.666)

b.

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

= 1.645 (((0.64*0.36) / 900)

= 0.026

E=0.026