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Chapter 9: Q. 11 (page 564)

The mean amount of liquid in the bottles is 179.6ml and the standard deviation is 1.3ml. A significance test yields a P-value of 0.0589. Interpret the P-value.

Short Answer

Expert verified

There is a 5.89%possibility that the mean volume of liquid in a sample of 40bottles is 179.6milliliters or more extreme, when the mean volume of liquid of all bottles is180 milliliters.

Step by step solution

01

Step 1. Given information

P=0.0589=5.89%x¯=179.6s=1.3

Claim mean is180

02

Step 2. Explanation

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population mean is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

H0:μ=180Ha:μ≠180

The P-value is the probability of getting the value of the test static or a value more extreme, when the null hypothesis is true.

There is a 5.89%possibility that the mean volume of liquid in a sample of 40bottles is 179.6milliliters or more extreme, when the mean volume of liquid of all bottles is 180milliliters.

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Most popular questions from this chapter

Interpreting a P-value A student performs a test of H0:p=0.3H0:p=0.3versus Ha:p<0.3Ha:p<0.3and gets a P-value of 0.22The student says, "This means there is about a22%chance that the null hypothesis is true." Explain why the student's explanation is wrong.

Making conclusions A student performs a test of H0:p=0.75versus Ha:p<0.75at α=0.05significance level and gets a P-value of 0.22

The student writes: “Because the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Significance tests A test of Ho:p=0.5versus Ha:p>0.5based on

a sample of size 200yields the standardized test statistic z=2.19. Assume that the conditions for performing inference are met.

a. Find and interpret the P-value.

b. What conclusion would you make at the α=0.01 significance level? Would

your conclusion change if you used α=0.05 instead? Explain your reasoning.

c. Determine the value of p^= the sample proportion of successes.

The standardized test statistic for a test of H0:p=0.4versus Ha:pnotequalto0.4isz=2.43This test is

a. not significant at either α=0.05or α=0.01

b. significant at α=0.05but not atα=0.01

c. significant atα=0.01but not at α=0.05

d. significant at both α=0.05andα=0.01

e. inconclusive because we don’t know the value of p^

Which of the following 95%confidence intervals would lead us to reject H0:p=0.30in favor of Ha:pnotequalto0.30at the 5%significance level?

a. (0.19,0.27)

b.(0.24,0.30)

c. (0.27,0.31)

d. (0.29,0.31)

e. None of these
See all solutions

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