This set of exercises focuses on how to set up the null and alternative hypotheses coreect;y. Please read the given story problem carefully to identify the claim and then choose the suitable forms if hypotheses. Once you have your own hypotheses, please check the answer and explanations to make sure you understand the relationship between the claim and the hypotheses.

Problem 1.   In the past, the mean running time for a certain type of flashlight battery has been 9 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result.

A) Ho: μ = 9.0 vs Ha: μ ≠ 9.0
B) Ho: μ = 9.0 vs Ha: μ > 9.0
C) Ho: μ ≠ 9.0 vs Ha: μ = 9.0
D) Ho: μ ≥ 9.0 vs Ha: μ = 9.0

Problem 2.   The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.6 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit.

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Problem 3.   The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. A hypothesis test is to be performed to decide whether adult women are, on average, getting less than the RDA of 75 milligrams per day.

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Problem 4.   The mean credit card debt among households in one state is $8400. A hypothesis test is to be performed to decide whether the mean credit card debt for households in the formerly affluent town of Rich-No-More differs from the mean credit card debt for the state.

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Problem 5.   A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.

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Problem 6.   At one school, the average amount of time that tenth-graders spend watching television each week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.

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Problem 7.   A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200 They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct.

A) Ho: μ = 1200 vs Ha: μ ≤ 1200
B) Ho: μ ≥ 1200 vs Ha: μ < 1200
C) Ho: μ > 1200 vs Ha: μ ≠ 12001
D) Ho: μ ≤ 1200 vs Ha: μ > 1200

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Problem 8.   In 1990, the mean duration of long-distance telephone calls originating in one town was 7.2 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the mean duration of long-distance phone calls has changed from the 1990 mean of 7.2 minutes.

A) Ho: μ = 7.2 vs Ha: μ ≤ 7.2
B) Ho: μ ≥ 7.2 vs Ha: μ < 7.2
C) Ho: μ = 7.2 vs Ha: μ ≠ 7.2
D) Ho: μ ≤ 7.2 vs Ha: μ > 7.2

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Problem 9.   The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a mean temperature, μ, of 45^oF, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and wants to conduct a hypothesis test to determine whether the true mean temperature differs from this value.

A) Ho: μ ≠ 45 vs Ha: μ ≤ 45
B) Ho: μ ≥ 45 vs Ha: μ < 45
C) Ho: μ = 45 vs Ha: μ ≠ 45
D) Ho: μ ≤ 45 vs Ha: μ > 45

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Problem 10.   A psychologist has designed a test to measure stress levels in adults. She has determined that nationwide the mean score on her test is 27. A hypothesis test is to be conducted to determine whether the mean score for trial lawyers exceeds the national mean score.

A) Ho: μ ≠ 27 vs Ha: μ ≤ 27
B) Ho: μ ≥ 27 vs Ha: μ < 27
C) Ho: μ = 27 vs Ha: μ ≠ 27
D) Ho: μ ≤ 27 vs Ha: μ > 27

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