Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q. 3.1

Expert-verified

The Practice of Statistics for AP

Found in: Page 644

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good indicator of decay. Lower strength means the fabric has decayed. For one part of the study, the researcher buried $10$ strips of polyester fabric in well-drained soil in the summer. The strips were randomly assigned to two groups: $5$ of them were buried for $2$ weeks and the other $5$ were buried for $16$ weeks. Here are the breaking strengths in pounds
Do the data give good evidence that polyester decays more in $16$ weeks than in $2$ weeks? Carry out an appropriate test to help answer this question .

The confidence interval is $(- 0.7561, - 0.5639)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

Given in the question that,

$\begin{aligned} n_{1} = 90, {\bar{x}}_{1} = 2.95, s_{1} = 0.22 \\ n_{2} = 45, {\bar{x}}_{2} = 3.61, s_{2} = 0.19 \end{aligned}$

Step 2: Explanation

According to the given data

$n_{1} = 90, {\bar{x}}_{1} = 2.95, s_{1} = 0.22$

$n_{2} = 45, {\bar{x}}_{2} = 3.61, s_{2} = 0.19$

To construct the confidence interval, follow the procedures supplied by the Ti-83 calculator:

1. Click on STAT $> T E S T S > 2$ -SampTInt

2. Click on Stats and enter the provided data set.

3. Select Polled: No and calculate

4. Press ENTER

The output obtained is

Most popular questions for Math Textbooks

To study the long-term effects of preschool programs for poor children, researchers designed an experiment. They recruited $123$ children who had never attended preschool from low-income families in Michigan. Researchers randomly assigned $62$ of the children to attend preschool (paid for by the study budget) and the other 61 to serve as a control group who would not go to preschool. One response variable of interest was the need for social services as adults. In the past $10$ years, $38$ children in the preschool group and $49$ in the control group have needed social services.

The Minitab output below gives a $95$ % conﬁdence interval for $p 1 - p 2$ . Interpret this interval in context. Then explain what additional information the conﬁdence interval provides.

A sample survey interviews SRSs of $500$ female college students and $550$ male college students. Each student is asked whether he or she worked for pay last summer. In all, $410$ of the women and $484$ of the men say “Yes.” Take $p_{M}$ and localid="1650271716184" $p_{F}$ be the proportions of all college males and females who worked last summer. We conjectured before seeing the data that men are more likely to work. The hypotheses to be tested are

(a) $H_{0} : p_{M} - p_{f} = 0$ versus $H_{a}; p_{M} - p_{F} \neq 0$

(b) $H_{0} : p_{M} - p_{F} = 0$ versus $H_{a} : p_{M} - p_{F} > 0$ .

(c) $H_{0} : p_{M} - p_{F} = 0$ versus $H_{a} : p_{M} - p_{F} < 0$

(d) $H_{0} : p_{M} - p_{F} > 0$ versus $H_{a} : p_{M} - p_{F} = 0$

(e) $H_{0} : p_{M} - p_{F} \neq 0$ versus $H_{a} : p_{M} - p_{F} = 0$

44. Tropical flowers Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds.

Researchers believe that over time, the lengths of the flowers and the forms of the hummingbirds’ beaks have evolved to match each other. Here are data on the lengths in millimeters for random samples of two color varieties of the same species of flower on the island of Dominica:

(a) A Fathom dotplot of the data is shown below. Use the graph to answer these questions:

Are the centers of the two groups similar or different? Explain
Are the spreads of the two groups similar or different? Explain.

(b) Construct and interpret a 95% confidence interval for the difference in the mean lengths of these two varieties of flowers.(c) Does the interval support the researchers’ belief that the two flower varieties have different average lengths? Explain.

A large university is considering the establishment of a schoolwide recycling program. To gauge interest in the program by means of a questionnaire, the university takes separate random samples of undergraduate students, graduate students, faculty, and staff. This is an example of what type of sampling design?

(a) Simple random sample

(b) Stratified random sample

(c) Convenience sample

(d) Cluster sample

(e) Systematic sample

A sample survey interviews SRSs of $500$ female college students and $550$ male college students. Each student is asked whether he or she worked for pay last summer. In all, 410 of the women and 484 of the men say “Yes.” The pooled sample proportion who worked last summer is about

(a) ${\overset{⏜}{p}}_{C} = 1.70$

(b) ${\hat{p}}_{C} = 0.89$

(c) ${\hat{p}}_{C} = 0.88$

(d) ${\hat{p}}_{C} = 0.85$

(e) ${\hat{p}}_{C} = 0.82$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free