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:

A)about 2.00≤μ≤2.26

B)about 2.11≤μ≤2.15

C)about 2.05≤μ≤2.21

D)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 = Z_0.01 = 2.326 ( Using z table    )

Margin of error = E = Z_/2    * ( /n)

= 2.326 * ( 0.11 /  36 )

=0.04
At 98% confidence interval mean
is,

- E < < + E
2.13 - 0.04 <   < 2.13 + 0.04

(2.09 , 2.17)