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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

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 7 鈥淧ulse Rates鈥�

In Exercises 1鈥�4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: 鈥淪hould Americans replace passwords with biometric security (fingerprints, etc)?鈥� Among the respondents, 53% said 鈥測es.鈥� We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Equivalence of Methods If we use the same significance level to conduct the hypothesis test using the P-value method, the critical value method, and a confidence interval, which method is not equivalent to the other two?

t Test Exercise 2 refers to a t test. What is the t test? Why is the letter t used? What is unrealistic about the z test methods in Part 2 of this section?

Using Technology. In Exercises 5鈥�8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use = 0.05 significance level and answer the following:

a. Is the test two-tailed, left-tailed, or right-tailed?

b. What is the test statistic?

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e. What is the final conclusion?

Biometric Security In a USA Today survey of 510 people, 53% said that we should replace passwords with biometric security, such as fingerprints. The accompanying Statdisk display results from a test of the claim that half of us say that we should replace passwords with biometric security.

In Exercises 1鈥�4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: 鈥淪hould Americans replace passwords with biometric security (fingerprints, etc)?鈥� Among the respondents, 53% said 鈥測es.鈥� We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Null and Alternative Hypotheses Identify the null hypothesis and alternative hypothesis.
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