Quarter Mile Times A consumer group claims that the mean min time it takes for a sedan to travel a quarter mile is greater than 14.7 seconds. A random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.4 seconds and a standard deviation of 2.10 seconds. At a do you have enough evidence to support the consumer group's claim? 0.10,

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question 27

**Section 7.3: Hypothesis Testing for the Mean (σ Unknown)**

**Page 385**

**Using a P-Value with a t-Test**

In Exercises 27-30:

(a) Identify the claim and state \( H_0 \) and \( H_a \).

(b) Use technology to find the P-value.

(c) Decide whether to reject or fail to reject the null hypothesis.

(d) Interpret the decision in the context of the original claim. Assume the population is normally distributed.

---

**Exercise 27: Quarter Mile Times**

A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.7 seconds. A random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.4 seconds and a standard deviation of 2.10 seconds. At \( \alpha = 0.10 \), do you have enough evidence to support the consumer group’s claim? 
*(Adapted from Zero to 60 Times)*

**Exercise 28: Dive Duration**

An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.5 minutes. A random sample of 34 dive durations has a mean of 12.2 minutes and a standard deviation of 2.2 minutes. Is there enough evidence to reject the claim at \( \alpha = 0.10 \)? 
*(Source: Marine Ecology Progress Series)*

**Exercise 29: Class Size**

You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table to the left. At \( \alpha = 0.05 \), can you support the university’s claim?

**Exercise 30: Faculty Classroom Hours**

The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table at the left. At \( \alpha = 0.01 \), can you reject the dean’s claim?
Transcribed Image Text:**Section 7.3: Hypothesis Testing for the Mean (σ Unknown)** **Page 385** **Using a P-Value with a t-Test** In Exercises 27-30: (a) Identify the claim and state \( H_0 \) and \( H_a \). (b) Use technology to find the P-value. (c) Decide whether to reject or fail to reject the null hypothesis. (d) Interpret the decision in the context of the original claim. Assume the population is normally distributed. --- **Exercise 27: Quarter Mile Times** A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.7 seconds. A random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.4 seconds and a standard deviation of 2.10 seconds. At \( \alpha = 0.10 \), do you have enough evidence to support the consumer group’s claim? *(Adapted from Zero to 60 Times)* **Exercise 28: Dive Duration** An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.5 minutes. A random sample of 34 dive durations has a mean of 12.2 minutes and a standard deviation of 2.2 minutes. Is there enough evidence to reject the claim at \( \alpha = 0.10 \)? *(Source: Marine Ecology Progress Series)* **Exercise 29: Class Size** You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table to the left. At \( \alpha = 0.05 \), can you support the university’s claim? **Exercise 30: Faculty Classroom Hours** The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table at the left. At \( \alpha = 0.01 \), can you reject the dean’s claim?
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