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Chapter 8: Q1 (page 407)

Distributions Using the methods of this chapter, identify the distribution that should be used for testing a claim about the given population parameter.

a. Mean

b. Proportion

c. Standard deviation

Short Answer

Expert verified

a. Normal Distribution (when 蟽 is known) and Student鈥檚 t distribution (when is unknown)

b.Normal Distribution

c.Chi-square Distribution

Step by step solution

01

Given information

Different claims are to be tested for different population parameters, and thus, different probability distributions are applied.

02

Testing a claim about the population mean

a.

If a claim about the population mean is to be tested, two distributions can be utilized:

Normal distribution

Student鈥檚 t distribution

A test statistic following the normal distribution is used to test the claim about the population mean when the population standard deviation is known.

A test statistic following the student鈥檚 t-distribution is used to test the claim about the population mean when the population standard deviation is unknown.

03

Testing a claim about the population proportion

b.

If a claim about the population proportion is to be tested, thenormal distribution is applied.

04

Testing a claim about the population standard deviation

c.

If a claim about the population standard deviation is to be tested, thechi-square distribution is applied.

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Most popular questions from this chapter

Testing Claims About Proportions. In Exercises 9鈥�32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. Should this be comforting to physicians?

What is the relation between the significance level of a hypothesis test and the probability of making a Type I error?

In Exercises 9鈥�12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Exercise 8 鈥淧ulse Rates鈥�

We have been provided a sample mean, sample size, and population standard deviation. In the given case, use the one-mean z-test to perform the required hypothesis test at the 5%significance level.

x炉=21,n=32,蟽=4,H0:渭=22,Ha:渭<22

Testing Claims About Proportions. In Exercises 9鈥�32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Super Bowl Wins Through the sample of the first 49 Super Bowls, 28 of them were won by teams in the National Football Conference (NFC). Use a 0.05 significance level to test the claim that the probability of an NFC team Super Bowl win is greater than one-half.
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