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Chapter 10: Q. 43 (page 666)

How do the numbers of people living in households in the United Kingdom (U.K.) and South Africa compare? To help answer this question, we chose independent random samples of 50students from each country. Here is a dot-plot of the household sizes reported by the students in the survey:

Let 渭UK = 渭UK=the true mean number of people living in U.K. households and role="math" localid="1664190023788" 渭SA=the true mean number of people living in South African households. Check if the conditions for calculating a confidence interval for 渭UK鈭捨糞A渭UK-渭SA are met.

Short Answer

Expert verified

All conditions are met.

Step by step solution

01

Step 1. Given information

Given:

02

Step 2. Calculation

We have to check if the conditions are met or not. Therefore,

There are three conditions to be satisfied:

Random: It is satisfied because the samples are independent random samples.

Independent: It is satisfied because it is given that the sample are independent and the sample size is less than10% of the population size.

Normal: It is not satisfied because the sample size of both the samples50 is at least 30.

Thus, all the conditions are satisfied.

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Most popular questions from this chapter

Thirty-five people from a random sample of 125 workers from Company A admitted

to using sick leave when they weren鈥檛 really ill. Seventeen employees from a random

sample of 68 workers from Company B admitted that they had used sick leave when

they weren鈥檛 ill. Which of the following is a 95% confidence interval for the difference

in the proportions of workers at the two companies who would admit to using sick

leave when they weren鈥檛 ill?

(a) 0.03卤(0.28)(0.72)125+(0.25)(0.75)68

(b) 0.03卤1.96(0.28)(0.72)125+(0.25)(0.75)68

(c) 0.03卤1.645(0.28)(0.72)125+(0.25)(0.75)68

(d) 0.03卤1.96(0.269)(0.731)125+(0.269)(0.731)68

(e)0.03卤1.645(0.269)(0.731)125+(0.269)(0.731)68

National Park rangers keep data on the bears that inhabit their park. Here is a histogram of the weights of bears measured in a recent year:

Which of the following statements is correct?

a. The median will lie in the interval (140,180), and the mean will lie in the interval(180,220).

b. The median will lie in the interval(140,180), and the mean will lie in the interval (260,300).

c. The median will lie in the interval(100,140), and the mean will lie in the interval (180,220).

d. The mean will lie in the interval (140,180),and the median will lie in the interval (260,300).

e. The mean will lie in the interval (100,140), and the median will lie in the interval (180,220).

Are teenagers going deaf? In a study of 3000randomly selected teenagers in 1990,450showed some hearing loss. In a similar study of 1800 teenagers reported in 2010,351showed some hearing loss.

a. Do these data give convincing evidence that the proportion of all teens with hearing

loss has increased at the 伪=0.01 significance level?

b. Interpret the P-value from part (a) in the context of this study.

Which of the following statements is false?

a. A measure of center alone does not completely summarize a distribution of quantitative data.

b. If the original measurements are in inches, converting them to centimeters will not change the mean or standard deviation.

c. One of the disadvantages of a histogram is that it doesn鈥檛 show each data value.

d. In a quantitative data set, adding a new data value equal to the mean will decrease the standard deviation.

e. If a distribution of quantitative data is strongly skewed, the median and interquartile range should be reported rather than the mean and standard deviation.

Two samples or paired data? In each of the following settings, decide whether you should use two-sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference. Explain your choice.

a. To test the wear characteristics of two tire brands, A and B, each of 50cars of the same make and model is randomly assigned Brand A tires or Brand B tires.

b. To test the effect of background music on productivity, factory workers are observed. For one month, each subject works without music. For another month, the subject works while listening to music on an MP3 player. The month in which each subject listens to music is determined by a coin toss.

c. How do young adults look back on adolescent romance? Investigators interviewed a random sample of 40couples in their mid-twenties. The female and male partners were interviewed separately. Each was asked about his or her current relationship and also about a romantic relationship that lasted at least 2months when they were aged 15or 16. One response variable was a measure on a numerical scale of how much the attractiveness of the adolescent partner mattered. You want to find out how much men and women differ on this measure.

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