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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 σ is known) and Student’s 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’s 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’s 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

P-Values. In Exercises 17–20, do the following:

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value. (See Figure 8-3 on page 364.)

c. Using a significance level of α = 0.05, should we reject H0or should we fail to reject H0?

The test statistic of z = 2.01 is obtained when testing the claim that p≠0.345.

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

How Many English Words? A simple random sample of 10 pages from Merriam-Webster’s Collegiate Dictionary is obtained. The numbers of words defined on those pages are found, with these results: n = 10, x = 53.3 words, s = 15.7 words. Given that this dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.0 words. Assume a normally distributed population. Use a 0.01 significance level to test the claim that the mean number of words per page is greater than 48.0 words. What does the result suggest about the claim that there are more than 70,000 defined words?

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?

In Exercises 1–4, 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: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Requirements and Conclusions

a. Are any of the three requirements violated? Can the methods of this section be used to test the claim?

b. It was stated that we can easily remember how to interpret P-values with this: “If the P is low, the null must go.” What does this mean?

c. Another memory trick commonly used is this: “If the P is high, the null will fly.” Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading?

d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like 0.0483?

Testing Claims About Proportions. In Exercises 9–32, 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.

Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Use a 0.01 significance level to test Mendel’s claim that under the same circumstances, 25% of offspring peas will be yellow. What can we conclude about Mendel’s claim?
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