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You are conducting a study of students doing work-study jobs on your campus
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1. You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are the following.

A. How many hours are you scheduled to work each week? Answer to the nearest hour.

B. How applicable is this work experience to your future employment goals?

      Respond using the following scale: 1= not at all, 2 = somewhat, 3 = very

(a) Suppose you take random samples from the following groups: freshmen, sophomores, juniors, and seniors. What kind of sampling technique are you using (simple random, stratified, systematic, cluster, multistage, convenience)?

cluster sample

systematic sample    

simple random sample

multistage sample

stratified sample

convenience sample

 

(b) Describe the individuals of this study.

Students on your campus with work-study jobs.

Students on all campuses with work-study jobs.    

Students on your campus.

Students on all campuses.

 

(c) What is the variable for question A?

number of students who work

total hours worked    

type of job

hours scheduled

 

Classify the variable as qualitative or quantitative.

neither quantitative nor qualitative

qualitative    

both qualitative and quantitative

quantitative

 

What is the level of measurement?

interval

ordinal    

ratio

nominal

 

(d) What is the variable for question B?

rating of applicability of work experience to future employment

rating of satisfaction of work experience for future employment    

hours scheduled

number of students who work

 

Classify the variable as qualitative or quantitative.

both qualitative and quantitative

qualitative    

neither quantitative nor qualitative

quantitative

 

What is the level of measurement?

ratio

interval    

ordinal

nominal

 

(e) Is the proportion of responses "3 = very" to question B a statistic or a parameter?

parameter

neither a statistic nor a parameter    

both a parameter and a statistic

statistic

 

 

(f) Suppose only 40% of the students you selected for the sample respond. What is the nonresponse rate?

%

Do you think the nonresponse rate might introduce bias into the study? Explain.

Yes, the people choosing to respond may have some characteristics that would bias the study.

No, the people choosing not to respond probably don't have characteristics that would bias the study.    

No, the people choosing to respond probably don't have characteristics that would bias the study.

Yes, the people choosing not to respond may have some characteristics that would bias the study.

 

(g) Would it be appropriate to generalize the results of your study to all work-study students in the nation? Explain.

No, results only apply to the students sampled.

No, the sample frame is restricted to one campus.    

Yes, the sample frame is for all campuses.

Yes, the sample is random so the results can be applied anywhere.

 

 

2. A radio talk show host asked listeners to respond either yes or no to the question, "Is the candidate who spends the most on a campaign the most likely to win?" Fifteen people called in and nine said yes. What is the implied population?

all radio listeners

all listeners of the radio talk show    

all callers

all adults

 

What is the variable?

opinion of a caller

opinion of a listener    

number of listeners

number of callers

 

Can you detect any bias in the selection of the sample?

Yes, nonresponse. Many listeners may not call in.

Yes, there is a systematic bias against those that are not listening to the talk show.    

Yes, voluntary response. Those with the strongest opinions are most likely to call in.

No, there is no bias in the selection of this sample.

 

3. Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researchers conducted a study of lawsuits involving 1908 businesses ranked in the Fortune 1000 over a 20-year period. They found the following distribution of civil justice caseloads brought before the federal courts involving the businesses. Note: Contracts cases involve disputes over contracts between businesses.

Case Type

Number of Filings

(in thousands)

Contracts

General torts (personal injury)

Asbestos liability

Other product liability

All other

107

191

  49

  38

  21

  1. Make a Pareto chart of the caseloads.

 

Which type of cases occur most frequently?

contracts

all other    

other product liability

general torts

asbestos liability

 

(b) Make a pie chart showing the percentage of cases of each type.

 

 

4. "Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L).

1.9

3

5.7

4.4

1.9

9

3.9

7.4

(a) Find the mean, median, and mode. (Round your answers to two decimal places.)

mean

 

median

 

mode

 

 

(b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.)

s

 

CV

%

range

 

 

5. Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:

x

1

2

3

4

5

y

15.4

19.1

14.4

19.6

20.0

Σx = 15; Σy = 88.5; Σx2 = 55; Σy2 = 1593.49; Σxy = 275.2

 

(a) Draw a scatter diagram.

 

(b) Find the equation of the least-squares line. (Round your answers to two decimal places.)

=___________

+ __________x

 

(c) Find r. Find the coefficient of determination r2. (Round your answers to three decimal places.)

r =

 

r2 =

 

 

(d) Explain what these measures mean in the context of the problem.

The correlation coefficient r measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The coefficient of determination r2 measures the explained variation in mortality rate by the corresponding variation in age of a bighorn sheep.

The correlation coefficient r2 measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The coefficient of determination r measures the explained variation in mortality rate by the corresponding variation in age of a bighorn sheep.    

Both the correlation coefficient r and coefficient of determination r2 measure the strength of the linear relationship between a bighorn sheep's age and the mortality rate.

The coefficient of determination r measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The correlation coefficient r2 measures the explained variation in mortality rate by the corresponding variation in age of a bighorn sheep.

 

6. Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the women interviewed, 24% had asked for a raise, and of those women who had asked for a raise, 45% received the raise. If a woman is selected at random from the survey population of women, find the following probabilities. (Enter your answers to three decimal places.)

(a) P(woman asked for a raise)

 

 

(b) P(woman received raise, given she asked for one)

 

 

(c) P(woman asked for raise and received raise)

 

7.According to Harper's Index, 45% of all federal inmates are serving time for drug dealing. A random sample of 19 federal inmates is selected.

(a) What is the probability that 12 or more are serving time for drug dealing? (Use 3 decimal places.)

 

 

(b) What is the probability that 7 or fewer are serving time for drug dealing? (Use 3 decimal places.)

 

 

(c) What is the expected number of inmates serving time for drug dealing? (Use 1 decimal place.)

 

 

 

8. According to the empirical rule, approximately what percentage of the area under a normal distribution lies within 1 standard deviation?

__________%

 

Within 2 standard deviations?

____%

 

Within 3 standard deviations?

____%

 

9. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.27 to $3.60. Use the fact that the confidence interval for the mean is in the form  − E to  + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places).

                                                E=$_______

 

10. The average annual miles driven per vehicle in the United States is 11.1 thousand miles, with σ≈ 600 miles. Suppose that a random sample of 26 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.8 thousand miles. Does this indicate that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average? Use a 0.05 level of significance.

 

What are we testing in this problem?

single proportion

single mean    

 

(a) What is the level of significance?

 

 

State the null and alternate hypotheses.

H0: p = 11.1; H1: p> 11.1

H0: μ = 11.1; H1: μ> 11.1    

H0: p = 11.1; H1: p≠ 11.1

H0: p = 11.1; H1: p< 11.1

H0: μ = 11.1; H1: μ≠ 11.1

H0: μ = 11.1; H1: μ< 11.1

 

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal, since we assume that x has a normal distribution with unknown σ.

The Student's t, since we assume that x has a normal distribution with known σ.    

The Student's t, since we assume that x has a normal distribution with unknown σ.

The standard normal, since we assume that x has a normal distribution with known σ.

 

What is the value of the sample test statistic? (Round your answer to two decimal places.)

 

 

 

(c) Find the P-value. (Round your answer to four decimal places.)

 

 

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

 

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the miles driven per vehicle in the city differs from the national average.

There is insufficient evidence at the 0.05 level to conclude that the miles driven per vehicle in the city differs from the national average.    

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