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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.80 (page 589)

Filling cola bottles Bottles of a popular cola are supposed to contain $300$ milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day’s production. The results are $299.4 297.7 301.0 298.9 300.2 297.0$

Short Answer

Expert verified

No, it is not possible to deduce that the average amount of cola in a bottle is less than 300 ml.

Step by step solution

01

; Given information

Given in the que $p$

role="math" localid="1650374125148"

t = \frac{\bar{x} - μ}{\frac{s}{\sqrt{n}}} = \frac{10 - 5}{\frac{12}{54}} = 90

02

Explanation

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Most popular questions from this chapter

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

a). $H_{0} : \hat{p} = 0.5; H_{a} : \hat{p} > 0.5$

(b) $H_{0} : p = 0.5; H_{a} : p > 0.5$

(c) $H_{0} : p = 0.5; H_{a} : p < 0.5$

(d) $H_{0} : p = 0.5; H_{a} : p \neq 0.5$

(e) $H_{0} : p > 0.5; H_{a} : p = 0.5$

We hear that listening to Mozart improves students’ performance on tests. Maybe pleasant odors have a similar effect. To test this idea, $21$ subjects worked two different but roughly equivalent paper-and-pencil mazes while wearing a mask. The mask was either unscented or carried a floral scent. Each subject used both masks, in a random order. The table below gives the subjects’ times with both masks.

Eye black Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does cye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black mines without eye black:

0.07	0.64	-0.12	-0.05	-0.18	0.14	-0.16	0.03
0.05	0.02	0.43	0.24	-0.11	0.28	0.05	0.29

We want to know whether cye black increases sensitivity an the average.

(a) State hypotheses, Be sure to define the parameter.

(b) Check conditions for carrying out a significance test.

(c) The $P v a l u e$ of the test is $0.047$ . Interpet this value in context.

- Interpret a Type l error and a Type ll error in context, and give the consequences of each.

- Understand the relationsonship between the significance level at a test P(Type li error), and power.

Ages of presidents Joe is writing a report on the backgrounds of American presidents. He looks up the ages of all the presidents when they entered office. Because Joe took a statistics course, he uses these numbers to perform a significance test about the mean age of all U.S. presidents. Explain why this makes no sense.

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?

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