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Chapter 8: Q1BSC (page 356)

Cans of coke data set 26 “cola weights and volumes” in appendix B includes volumes of regular coke. Based on that data set, assume that the cans are produced so that the volumes have a standard deviation of 0.115 oz. A new filling process is being tested for filling cans of cola, and a random sample of volumes is listed below. The sample has these summary statistics: \({\bf{n = 10,\bar x = 12}}{\bf{.0004}}\)oz. If we want to use the sample data to test the claim that the sample is form a population with standard deviation equal to 0.115 oz, what requirements must be satisfied? How does the normality requirement for a hypothesis test of a claim about a standard deviation differ from the normality requirement for a hypothesis test of a claim about a standard deviation differ from the normality requirement for a hypothesis test a claim about a mean?

12.078 11.851 12.108 11.760 12.142 11.779 12.397 11.504 12.147 12.238

Short Answer

Expert verified

The requirements are simple random samplesandanormally distributed population.

The condition for normal distribution is strict in the case of tests for claims about standard deviation or variance.

Step by step solution

01

Step-1: Given information

The study requires to test population standard deviation measure equal to 0.115 oz.

02

Step-2: State the requirements

As the testisconcernedwiththeclaim for population standard deviation, the chi-square test for standard deviation or variancesmustbe implemented.

The requirements areas follows:

Simple random sample

Normally distributed population or sample size larger than 30.

03

Step-3: Compare the requirements with that of mean

The test for mean hasthesame requirementsassimple random samplesandanormally distributed population.

The condition for normality in the case of claims about population standard deviation is more strict than the claims about the mean.

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