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Chapter 9: Q.99 (page 592)

The reason we use tprocedures instead of zprocedures when carrying out a test about a population mean is that

(a) zcan be used only for large samples.

(b)zrequires that you know the population standard deviation σ.

(c) zrequires you to regard your data as an SRS from the population.

(d) zapplies only if the population distribution is perfectly Normal.

(e) zcan be used only for confidence intervals.

Short Answer

Expert verified

The reason we use tprocedures instead of zprocedures when carrying out a test about a population mean is that (c)z requires you to regard your data as an SRS from the population.

Step by step solution

01

Step-1 Given Information

Given in the question that The reason we use tprocedures instead of zprocedures when carrying out a test about a population mean is that we have to fin out taht which option is correct.

02

Step-2 Explanation

There are two tests ztest and ttest. The reason of using the tprocedures instead of ztest is required to discuss here.

z-test and t-test are defined as statistical procedures that are used to determine whether the sample mean differs from the population mean or not. It must be noted that z-test is preferred to use when the standard deviation of the population is given, and t-test is used the standard deviation of the population is not given.

The correct option is (c).

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Most popular questions from this chapter

Sweetening colas Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of 10batches of a new cola recipe:

2.00.40.72.0-0.42.2-1.31.21.12.3

Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.

(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.

(b) Describe a Type I error and a Type II error in this setting and explain the consequences of each.

(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests—H0:μ=6.7versusHa:μ<6.7 or the one from part (a) of this exercise—would you be

more interested in? Justify your answer.

Normal body temperature (8.3) Check that the conditions are met for performing inference about the mean body temperature in the population of interest.

Roulette an American roulette wheel has 18red slots among its 38slots.In a random sample of 50pins,the ball lands in a red slot 31times.

(a) Do the data give convincing evidence that the wheel is unfair? Carry out an appropriate test at theα=0.05significance level to help answer this question.

(b) The casino manager uses your data to produce a 99%confidence interval for pand gets role="math" localid="1650358305073" 0.44,0.80. He says that this interval provides convincing evidence that the wheel is fair. How do you respond?

- If conditions are met, conduct a one-sample \(t\) test about a population mean \(\mu\).

For the job satisfaction study described in Section 9.1, the hypotheses are

H0∶μ=0Ha:μ≠0

where μis the mean difference in job satisfaction scores (self-paced - machine-paced) in the population of assembly-line workers at the company? Data from a random sample of 18workers gave x=17andsx=60

Use Table B to find the P-value. What conclusion would you draw?
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