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Chapter 9: Q.2 (page 597)

You are thinking of conducting a one-sample t-test about a population mean M using a 0.05 significance level. You suspect that the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct?

(a) You should not carry out the test because the population does not have a Normal distribution.

(b) You can safely carry out the test if your sample size is large and there are no outliers.

(c) You can safely carry out the test if there are no outliers, regardless of the sample size.

(d) You can carry out the test only if the population standard deviation is known.

(e) The t procedures are robust鈥攜ou can u

Short Answer

Expert verified

The correct statement is (B), You can safely carry out the test if your sample size is large and there are no outliers.

Step by step solution

01

Given Information

A one-sample ttest about a population mean Musing a 0.05 significance level.

02

Explanation

To identify the correct statement:

(a) False, because if a distribution is moderately skewed, then you can still carry out the test if the sample size is large (30or more).

(b) True, because if the sample size is larger (30 or more) and there are no outliers, then you can still safely carry out the test.

(c) False, the sample size should be large (30 or more) since the distribution is moderately skewed.

(d) False, the one-sample t test can only be used if the population standard deviation is unknown. You apply the onesample z test if the population standard deviation is known.

(e) False, t-procedures are not robust, because they are heavily influenced by outliers.

Therefore, the correct answer is (B).

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Most popular questions from this chapter

Does this paper give convincing evidence that the mean amount of sugar in the hindguts under these conditions is not equal to 7mg? Justify your answer.

Is your food safe? Do you feel confident or not confident that the food available at most grocery stores is safe to eat? when a gallup poll asked this question, 87%of the sample said they were confident." Callup announced the poll's margin of error for 95%confidence as卤3 percentage points. Which of the following sources of error are included in this margin of error? Explain.

(a) Gallup dialed landline telephone numbers at random and so missed all people without landline phones, including people whose only phone is a cell phone.

(b) Some people whose numbers were chosen never answered the phone in several calls or answered but refused to participate in the poll.

(c) There is chance variation in the random selection of telephone numbers.

Refer to Exercise 2. For Yvonne's survey, 96 students in the sample said they rarely or never argue with friends. A significance test yields a P-value of 0.0291.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.

The z statistic for a test of H0 :p = 0.4 versus Ha : p > 0.4 is z = 2.43. This test is

(a) not significant at either 伪=0.05or 伪=0.01.

(b) significant at 伪=0.05but not at 伪=0.01

(c) significant at 伪=0.01but not at 伪=0.05.

(d) significant at both 伪=0.05and 伪=0.01.

(e) inconclusive because we don鈥檛 know the value of 藛p .

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 蟽.

(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.
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