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Chapter 8: Q3BSC (page 356)

Cans of coke for the sample data from exercise 1, we get “P-value<0.01” when testing the claim that the new filling process results in volumes with the same standard deviation of 0.115 oz.

a. What should we conclude about the null hypothesis?

b. What should we conclude about the original claims?

c. What do these results suggest about the new filling process?

Short Answer

Expert verified

a. The null hypothesis is rejected ata0.01 level of significance.

b. There is notsufficient evidence to support the null hypothesis.

c. The result suggests that the variation in the volume is different from 0.115 oz, which implies the volume is not consistent.

Step by step solution

01

Step-1: Given information

Refer to the data in exercise 1 for the volume of the new filling process.

02

Step-2: State the hypotheses

a.

Let \(\sigma \)be the population standard deviation of the volumes of new filling processes.

\(\begin{array}{l}{H_0}:\sigma = 0.115\\{H_1}:\sigma \ne 0.115\end{array}\)

03

Step-3: State the decision

b.

The decision rule statesif the p-value is lesser than 0.01, the null hypothesis is rejected. Otherwise, the null hypothesis is failed to be rejected.

The p-value is lesser than 0.01. Thus, the null hypothesis is rejected. Hence, it can be concluded that there is not sufficient evidence to support the claim.

04

Step-4: Compute the test statistic

c.

The result suggests that the volume is inconsistent throughout all cans from the new filling process. Thus, the standard deviation is different from 0.115 oz.

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Most popular questions from this chapter

P-Values. In Exercises 17–20, do the following:

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value. (See Figure 8-3 on page 364.)

c. Using a significance level of α = 0.05, should we reject H0or should we fail to reject H0?

The test statistic of z = -2.50 is obtained when testing the claim that p<0.75

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

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Hypothesis Test with Known σ How do the results from Exercise 13 “Course Evaluations” change if σis known to be 0.53? Does the knowledge of σ have much of an effect?

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Cans of coke for the sample data from exercise 1, we get “P-value<0.01” when testing the claim that the new filling process results in volumes with the same standard deviation of 0.115 oz.

  1. What should we conclude about the null hypothesis?
  2. What should we conclude about the original claims?
  3. What do these results suggest about the new filling process?
See all solutions

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