7 A clothing company produces denim jeans The jeans are made

7. A clothing company produces denim jeans. The jeans are made and sold with either a regular cut or a boot cut. To estimate the proportion of customers in Tacoma. Washington, who prefer boot-cut jeans, a marketing researcher examined sales receipts for a random sample of 212 customers who purchased Jeans from the company\'s Tacoma, Washington, store. Thirty-four of the customers in the sample purchased boot-cut jeans. Construct a 99% confidence interval to estimate the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans.

Solution

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=34
Sample Size(n)=212
Sample proportion = x/n =0.1604
Confidence Interval = [ 0.1604 ±Z a/2 ( Sqrt ( 0.1604*0.8396) /212)]
= [ 0.1604 - 2.58* Sqrt(0.0006) , 0.1604 + 2.58* Sqrt(0.0006) ]
= [ 0.0954,0.2254] ~ [ 9.54%, 22.54% ]