Question

A random sample of 31 ice cream cones from McDonald's was weighted, the sample mean weight was 3.5 ounces with a standard deviation of 0.75 ounces. Construct a 99% confidence interval to estimate the overall mean weight of McDonald's ice cream cones. (Round your intermediate steps to 4 decimal places, and final answer to 2 decimal places) (10 points)

Answer 1

solution

Given that,

= 3.5

s =0.75

n = 31

Degrees of freedom = df = n - 1 =31 - 1 =30

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,30 = 2.750 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.750* ( 0.75/ 31) = 0.37

The 99% confidence interval estimate of the population mean is,

- E < < + E

3.5 - 0.37< <3.5 + 0.37

3.13< <3.87

( 3.13,3.87 )