Question

Alison, the owner of a regional chain of pizza stores, is trying to decide whether to add calzones to the menu. She conducts a survey of 700 people in the region and asks whether they would order calzones if they were on the menu. 46 people responded “yes.” Create a 90% confidence interval for the proportion of people in the region who would order calzones if they were on the menu.Round your answer to four decimal places.

Answer 1

Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 700

x = 46

p = 46/700 = 0.066

q = 1 - 0.066 = 0.934

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 1.645. Thus, the z score for a confidence level of 90% is 1.645

Therefore, the 90% confidence interval is

0.066 ± 1.645√(0.066)(0.934)/700

= 0.066 ± 0.0094

The lower limit of the confidence interval is

0.066 - 0.0094 = 0.0566

The upper limit of the confidence interval is

0.066 + 0.0094 = 0.0754