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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

Restaurant power problems Refer to Exercises 86 and 88

a. Explain one disadvantage of using 伪=0.10 instead of 伪=0.05 when

performing the test.

b. Explain one disadvantage of taking a random sample of 50 people instead of 30 people.

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential site. Based on the mean income of this sample, you will perform a test at the

伪=0.05 significance level of H0:渭=\)85,000versus Ha:渭>\(85,000, where 渭 is the true mean income in the population of people who live near the restaurant. The power of the test to detect that 渭=\)86,000is 0.64 Interpret this value.

Roulette An American roulette wheel has 18red slots among its 38slots. To test if a particular roulette wheel is fair, you spin the wheel 50times and the ball lands in a red slot 31times. The resulting P-value is0.0384.

a. Interpret the P-value.

b. What conclusion would you make at the伪=0.05 level?

c. The casino manager uses your data to produce a99% confidence interval for p and gets(0.44,0.80). He says that this interval provides convincing evidence that the wheel is fair. How do you respond

Significance tests A test of Ho:p=0.5versus Ha:p>0.5based on

a sample of size 200yields the standardized test statistic z=2.19. Assume that the conditions for performing inference are met.

a. Find and interpret the P-value.

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

your conclusion change if you used 伪=0.05 instead? Explain your reasoning.

c. Determine the value of p^= the sample proportion of successes.

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100
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