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Chapter 9: Q2CRE (page 414)

Family Heights. In Exercises 1–5, use the following heights (in.) The data are matched so that each column consists of heights from the same family.
Father
68.0
68.0
65.5
66.0
67.5
70.0
68.0
71.0
Mother
64.0
60.0
63.0
59.0
62.0
69.0
65.5
66.0
Son
71.0
64.0
71.0
68.0
70.0
71.0
71.7
71.0
Scatterplot Construct a scatterplot of the father/son heights, then interpret it.

Short Answer

Expert verified

The scatterplot is shown below:

There is no relationship between the height of the father and the son.

Step by step solution

01

Given information

The heights of three members of a family are studied.

Father	68.0	68.0	65.5	66.0	67.5	70.0	68.0	71.0
Mother	64.0	60.0	63.0	59.0	62.0	69.0	65.5	66.0
Son	71.0	64.0	71.0	68.0	70.0	71.0	71.7	71.0

02

Steps to sketch a scatterplot

A scatterplot is sketched for paired values in the dataset where one value is scaled corresponding to the variable on the horizontal axis and the other corresponding to the vertical axis.

Steps to sketch a scatterplot:

Mark two axis; horizontal for the father's height and vertical for the son’s height.
Mark the coordinates of height for two variables on the plot.

The resultant scatterplot is shown below.

03

Interpret the plot

From this scatterplot, thefollowing observations are made:

The dots do not follow any specific pattern.
The dots are clusters in the range of 68 to 72 inches vertically.

Thus, it can be inferred that there is no association between the heights of the father and the son.

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Most popular questions from this chapter

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of $n_{1} - 1$ and $n_{2} - 1$ .)

Are Male Professors and Female Professors Rated Differently?

a. Use a 0.05 significance level to test the claim that two samples of course evaluation scores are from populations with the same mean. Use these summary statistics: Female professors:

n = 40, $\bar{x}$ = 3.79, s = 0.51; male professors: n = 53, $\bar{x}$ = 4.01, s = 0.53. (Using the raw data in Data Set 17 “Course Evaluations” will yield different results.)

b. Using the summary statistics given in part (a), construct a 95% confidence interval estimate of the difference between the mean course evaluations score for female professors and male professors.

c. Example 1 used similar sample data with samples of size 12 and 15, and Example 1 led to the conclusion that there is not sufficient evidence to warrant rejection of the null hypothesis.

Do the larger samples in this exercise affect the results much?

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of $n_{1} - 1$ and $n_{2} - 1$ .) Car and Taxi Ages When the author visited Dublin, Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distribution), he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages can be found from the license plates. (There is no end to the fun of traveling with the author.) The ages (in years) are listed below. We might expect that taxis would be newer, so test the claim that the mean age of cars is greater than the mean age of taxis.

Car

Ages

4

0

8

11

14

3

4

4

3

5

8

3

3

7

4

6

6

1

8

2

15

11

4

1

1

8

Taxi Ages

8

8

0

3

8

4

3

3

6

11

7

7

6

9

5

10

8

4

3

4

Using Confidence Intervals

a. Assume that we want to use a 0.05 significance level to test the claim that p1 < p2. Which is better: A hypothesis test or a confidence interval?

b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method?

c. If we want to use a 0.05 significance level to test the claim that p1 < p2, what confidence level should we use?

d. If we test the claim in part (c) using the sample data in Exercise 1, we get this confidence interval: -0.000508 < p1 - p2 < - 0.000309. What does this confidence interval suggest about the claim?

Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

Bednets to Reduce Malaria In a randomized controlled trial in Kenya, insecticide-treated bednets were tested as a way to reduce malaria. Among 343 infants using bednets, 15 developed malaria. Among 294 infants not using bednets, 27 developed malaria (based on data from “Sustainability of Reductions in Malaria Transmission and Infant Mortality in Western Kenya with Use of Insecticide-Treated Bed nets,” by Lind blade et al., Journal of the American Medical Association, Vol. 291, No. 21). We want to use a 0.01 significance level to test the claim that the incidence of malaria is lower for infants using bed nets.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. Based on the results, do the bed nets appear to be effective?

Find and interpret 95 % confidence interval for the proportion of all US adults who never clothes-shop online.

See all solutions

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