Question

A sausage company in Sheboygan produces small sausage sandwiches. The company is interested in knowing the average retail price charged for this item in stores across the country. A stats bro that works for the company contacts 36 retailers and find that the average price is $2.13, and the standard deviation is $0.11. Which of the following is the 98% confidence interval around the price.

Group of answer choices

about 2.00≤μ≤2.26

about 2.11≤μ≤2.15

about 2.05≤μ≤2.21

about 2.09≤μ≤2.17

We do not have an adequate table to do this problem

Answer 1

Solution :

Given that,

Point estimate = sample mean = =$2.13

Population standard deviation =    = $0.11

Sample size = n =36

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * ( 0.11 /  36 )

= 0.0426
At 98% confidence interval estimate of the population mean
is,

- E ≤μ≤ + E

2.13 - 0.0426 ≤μ≤ 2.13+ 0.0426

2.09≤μ≤ 2.17