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Chapter 9: Q 102. (page 610)

The reason we use t procedures instead of z procedures when carrying out a test about a population mean is that

a. z requires that the sample size be large.

b. z requires that you know the population standard deviation 蟽

c. z requires that the data come from a random sample.

d. z requires that the population distribution be Normal.

e. z can only be used for proportions.

Short Answer

Expert verified

The correct option is (b).

Step by step solution

01

Given information

When doing a test on a population mean, we employ t procedures rather than z procedures for several reasons.

02

Explanation

The best answer for the given statement is 鈥� z requires that you know the population standard deviation 蟽鈥�. So the correct option is (b).

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Most popular questions from this chapter

A company that manufactures classroom chairs for high school students

claims that the mean breaking strength of the chairs is 300 pounds. One of the chairs collapsed beneath a 220-pound student last week. You suspect that the manufacturer is exaggerating the breaking strength of the chairs, so you would like to perform a test of H0:渭=300Ha:渭<300where 渭 is the true mean breaking strength of this company鈥檚 classroom chairs.

a. The power of the test to detect that 渭=294 based on a random sample of 30

chairs and a significance level of 伪=0.05 is 0.71. Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

Packaging DVDs (6.2,5.3) A manufacturer of digital video discs (DVDs) wants to be sure that the DVDs will fit inside the plastic cases used as packaging. Both the cases and the DVDs are circular. According to the supplier, the diameters of the plastic cases vary Normally with mean 渭=5.3inches and standard deviation 蟽=0.01inch. The DVD manufacturer produces DVDs with mean diameter渭=5.26inches. Their diameters follow a Normal distribution with 蟽=0.02inch.

a. Let X = the diameter of a randomly selected case and Y = the diameter of a randomly selected DVD. Describe the shape, center, and variability of the distribution of the random variable X鈭扽. What is the importance of this random variable to the DVD manufacturer?

b. Calculate the probability that a randomly selected DVD will fit inside a randomly selected case.

c. The production process runs in batches of 100 DVDs. If each of these DVDs is paired with a randomly chosen plastic case, find the probability that all the DVDs fit in their cases.

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is 0.975pound.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in part (a) is 0.0806. Interpret the P-value.

d. What conclusion would you make at the 伪=0.01 significance level?

Better parking A local high school makes a change that should improve student

satisfaction with the parking situation. Before the change, 37%of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of 200from the more than 2500students at the school. In all, 83students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Is there convincing evidence that the principal鈥檚 claim is true?

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

邪.H0:p鈭�=0.5;Ha:p鈭�>0.5H0:p^=0.5;Ha:p^>0.5.

b. H0:p=0.5;Ha:p>0.5H0:p=0.5;Ha:p>0.5.

c. H0:p=0.5;Ha:p<0.5H0:p=0.5;Ha:p<0.5.

d. H0:p=0.5;Ha:p鈮�0.H0:p=0.5;Ha:p鈮�0.5.

e. H0:p>0.5;Ha:p=0.5H0:p>0.5;Ha:p=0.5.
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