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Chapter 8: Q. 115 (page 489)

Use the following information to answer the next two exercises: A quality control specialist for a restaurant chain takes a random sample of size 12to check the amount of soda served in the 16oz. serving size. The sample mean is 13.30with a sample standard deviation of 1.55. Assume the underlying population is normally distributed.

Find the 95%Confidence Interval for the true population mean for the amount of soda served.

a.(12.42,14.18)b.(12.32,14.29)c.(12.50,14.10)

d. Impossible to determine

Short Answer

Expert verified

b.(12.32,14.29)

Step by step solution

01

Given information

A quality control specialist for a restaurant chain takes a random sample of size 12to check the amount of soda served in the 16oz. serving size.

The sample mean is 13.30with a sample standard deviation of 1.55.

02

Explanation

The confidence interval will be μ+/−tσ/n

μ=13.30σ=1.55n=12

We use a t-distribution rather than zbecause the population standard deviation isn't known and the sample size is <30

degrees of freedom =12-1=11

two tailedalpha=0.05(1-0.95)

so on a TI-842ndvars invt area=0.975

localid="1650542364085" df=11;t=2.26

you can calculate the confidence interval(12.32,14.29)

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