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?

Name: question 27 **Section 7.3: Hypothesis Testing for the Mean (σ Unknown)
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Description: 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

27) (a) The summary of statistics is The type of test is right tailed test The value of test statistic is, The degree of freedom is, df=n-1 =22-1 =21(b) The p-value of the hypothesis test is, (c) Since the p-value less than the level of significance, so we reject the null hypothesis at specified significance level. (d) Conclusion: Hence there is sufficient evidence to support the claim that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.7 seconds.

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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,

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,

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.

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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?

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