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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

Chapter 9: Q.104 (page 593)

The most important condition for sound conclusions from statistical inference is that
(a) the data come from a well-designed random sample or randomized experiment
(b) the population distribution be exactly Normal.
(c) the data contain no outliers.
(d) the sample size be no more than $10 %$ of the population size.
(c) the sample size be at least $30$ .

Short Answer

Expert verified

(a) the data come from a well-designed random sample or randomized experiment.

Step by step solution

01

Step-1: Given Information

We have to find out the correct option of the most important condition for sound conclusions from statistical inference.

02

Step-2 Explanation

The most significant criterion for using a significant test is that the data from the survey or sample originates from a random sample.

Hence, the correct option is (a)

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Most popular questions from this chapter

Improving health A large company's medical director launches a health promotion campaign to encourage employees to exercise more and eat better foods. One measure of the effectiveness of such a program is a drop in blood pressure. The director chooses a random sample of $50$ employees and compares their blood pressures from physical cams given before the campaign and again a year later. The mean change (after - before) in systolic blood pressure for these $50$ employees is $- 6$ and the standard deviation is $19.8$ .

(a) Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year? Carry out a test at the $α = 0.05$ significance level.

(b) Can we conclude that the health campaign caused a decrease in blood pressure? Why or why not?

Explain in plain language why a significance test that is significant at the 1% level must always be significant at the 5% level. If a test is significant at the 5% level, what can you say about its significance at the 1% level?

An SRS of 100 postal employees found that the average time these employees had worked at the postal service was $7$ years with standard deviation $2$ years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of $7.5$ that was true $20$ years ago? To determine this, we test the hypotheses $H_{0} : μ = 7.5$ versus $H_{a} : μ \neq 7.5$ using a one-sample $t$ test. What conclusion should we draw at the $5 %$ significance level?

(a) There is convincing evidence that the mean time working with the postal service has changed.

(b) There is not convincing evidence that the mean time working with the postal service has changed.

(c) There is convincing evidence that the mean time working with the postal service is still $7.5$ years.

(d) There is convincing evidence that the mean time working with the postal service is now $7$ years.

(e) We cannot draw a conclusion at the $5 %$ significance level. The sample size is too small.

A change is made that should improve student satisfaction with the parking situation at your school. Right now, 37% of students approve of the parking that’s provided. The null hypothesis $H_{0} : \hat{p} = 0.37$ is tested against the alternative $H_{d} : \hat{p} \neq 0.37$ .

Would the hypothesis that $μ = 5 mg$ be rejected at the $5 %$ level in favor of a two-sided alternative? Justify your answer.

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