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Chapter 8: Q2 (page 405)

Cans of coke use the data and the claim given in exercise 1 to identify the null and alternative hypothesis and the test statistic. What is the sampling distribution of the test statistic?

Short Answer

Expert verified

The hypotheses areas follows:

Ho:σ=0.115H1:σ≠0.115

The test statistic would follow chi-square distribution and has a value of 49.024 with 9 degrees of freedom.

Step by step solution

01

Step-1: Given information

Refer to example 1 for summary statistics.

n=10,x¯=12.0004oz,s=0.115oz

Claim states that the standard deviation for the population is equal to 0.115 oz.

02

Step-2: State the hypothesis

Let σbe the actual standard deviation of the population.

The hypotheses are formulated asfollows:

Ho:σ=0.115H1:σ≠0.115

03

Step-3: Describe the test statistic

The test statistic for the claim would follow the chi-square distribution with n-1 degrees of freedom.

The formula forthetest statistic isas follows:

χ2=n-1s2σ2=10-10.268420.1152=49.024

The degree of freedom isas follows:

df=n-1=10-1=9

Thus, the test statistic value is 49.024 with 9 degrees of freedom.

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