Name: ______________________ Class: _________________ Date: _________ ID: A

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STAT 2601/STAT 2625 Practice Final Exam Problems - Math Assistance Center

____ 1. The higher the value of the coefficient of determination, the greater the evidence for a causal relationship between x and y.

____ 2. Which of the following statistical studies is an observational study? a. A group of students is surveyed to determine the percentage who believe in

reincarnation.b. A random sample of students is shown a documentary on the evolution of

reincarnation beliefs throughout human history. A second random sample is not shown the documentary. The object of the study is to determine whether viewing the documentary affects belief in reincarnation.

c. To determine whether Vitamin C has any effectiveness at lessening the duration of the common cold, one set of cold sufferers is given no Vitamin C, a second set is given 2 grams per day, and a third set is given 5 grams of Vitamin C per day.

d. All of these studies are observational.e. None of these studies is observational.

____ 3. Which of the following statistical studies is an experimental study?

a. A researcher observes the effect of alcohol consumption on reaction time by administering various quantities of alcohol to randomly-selected subjects.

b. A study is conducted to see if exposure to increased carbon dioxide levels increases tomato yields.Tomato plants are selected at random and are then exposed to various doses of carbon dioxide.

c. Two random samples of senior adults are selected. The first group watches a 30-minute presentation on medicare fraud, while the other group does not watch the presentation. A survey is then administered to measure the level of confidence the subjects have in their health care providers.

d. All of these are experimental studies.e. None of these are experimental studies.

____ 4. Select the correct sampling method for the following situation.

To analyze the level of employee satisfaction at stores in a certain large city, a grocery store chain selects eight store locations at random and surveys all employees at these locations.

a. Simple random samplingb. Stratified random samplingc. Cluster samplingd. Systematic samplinge. Convenience sampling

Name: ______________________ ID: A

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____ 5. A survey form solicited the following responses:

I). age of respondentII). gender of respondentIII). level of job satisfaction (completely dissatisfied/somewhat dissatisfied/somewhat

satisfied/completely satisfied)IV). annual income

Which of the responses represent categorical data?

a. I onlyb. II onlyc. III onlyd. II and III onlye. All the responses are categorical.

Name: ______________________ ID: A

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____ 6. The following relative frequency distribution summarizes student responses to the question “If you could make your college choice over, would you still choose to enroll at your current college?”

Response Relative FrequencyDefinitely yes 0.45Probably yes 0.33Probably no 0.13Definitely no 0.09

Which of the following is the correct bar chart for the response data?

a. d.

b. e.

c.

Name: ______________________ ID: A

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____ 7. Which of the following variables are discrete?

I). the volume of liquid in a 16-ounce bottle of soda popII). the percentage of males 18-25 who actively view online pornographyIII). the number of broken eggs in a package of a dozen eggsIV). a count of the statistics majors at a certain university

a. II onlyb. II and III onlyc. III and IV onlyd. I onlye. All of these variables are discrete.

____ 8. According to the stem-and-leaf display below, how many times does the number 58 appear in the data set?

a. 0b. 1c. 2d. 5e. 58

____ 9. Which of the following stem and leaf plots corresponds a data distribution that is positively (right) skewed?

I. II. III.

a. I onlyb. II onlyc. III onlyd. I and III onlye. None of the distributions is positively skewed.

Name: ______________________ ID: A

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____ 10. The annual household incomes, in thousands of dollars, for 150 households in a small community are summarized in the histogram below.

What proportion of households have annual incomes of $90,000 or more?

a. 0.85b. 0.67c. 0.08d. 0.15e. 0.11

____ 11. The frequency distribution shown summarizes data on the percentage of college students enrolled in public institutions for the 50 U.S. states.

Percentage Enrolled Frequency40 to < 50 150 to < 60 560 to < 70 270 to < 80 1180 to < 90 2590 to < 100 6

What is the relative frequency for the 70 to < 80 interval?

a. 0.05b. 0.10c. 0.22d. 11e. 50

Name: ______________________ ID: A

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____ 12. The dot plot below shows the annual salaries, in thousands of dollars, of a sample of non-management staff who work for a small banking company.

Which of the following statistics would be the most reasonable estimate of the typical annual salary?

a. meanb. modec. mediand. interquartile rangee. range

____ 13. The table below summarizes the number of minutes spent exercising each day for a sample of 30 female college students.

Construct a graphical display of the data distribution and then indicate what summary measures you would use to describe center and spread.

a. center = mean; spread = standard deviationb. center = mean; spread = interquartile rangec. center = median; spread = standard deviationd. center = median; spread = interquartile rangee. center = mode; spread = range

____ 14. Costs per serving (in cents) for 16 high-fiber cereals rated very good or good by Consumer Reports are shown below:

40 48 60 46 20 78 70 31 50 54 69 45 50 30 60 20

Compute the mean and standard deviation for the above data set.

a. x = 50.4 cents; s = 11.1 centsb. x = 40.4 cents; s = 15.1 centsc. x = 19.4 cents; s = 12.1 centsd. x = 30.4 cents; s = 10.1 centse. x = 48.2 cents; s = 17.2 cents

Name: ______________________ ID: A

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____ 15. Data on tipping percent for 20 restaurant tables are:

0.0 6.0 40.0 30.9 12.9 11.4 56.2 60.0 11.0 15.6

40.4 25.0 27.7 28.9 106.0 20.0 11.0 30.1 15.1 16.0

Compute the value of the median for the above data set.

a. The median tipping percentage is 20%.b. The median tipping percentage is 22%.c. The median tipping percentage is 22.5%.d. The median tipping percentage is 23.5%.e. The median tipping percentage is 28.2%.

____ 16. Data on weekday exercise time (in minutes) for 20 males are shown below. Compute the interquartile range.

Male-Weekday54.5 90.5 3.5 0.0 0.0 27.5 197.5 58.0 140.5 9.0

10.0 30.0 0.0 70.0 30.5 0.0 53.0 153.5 9.0 0.0

a. 56.6b. 58.6c. 64.75d. 62.25e. 67.5

Name: ______________________ ID: A

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____ 17. Which of the five boxplots shown in figure corresponds to a data set with the 5-number summary below?

Minimum: 60Lower Quartile: 69Median: 76Upper Quartile: 82Maximum: 89

a. Boxplot 1b. Boxplot 2c. Boxplot 3d. Boxplot 4e. Boxplot 5

____ 18. Suppose that the distribution of weekly water usage for single-family homes in a particular city is mound shaped and approximately symmetric. The mean is 1,300 gallons, and the standard deviation is 200 gallons.

What is the approximate value of the 98th percentile?

a. 1,700 gallonsb. 1,100 gallonsc. 1,500 gallonsd. 1,900 gallonse. 1,300 gallons

Name: ______________________ ID: A

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____ 19. The mean number of text messages sent per month by customers of a cell phone service provider is 1,850, and the standard deviation is 800. Find the z-score associated with 3,000 messages sent. a. z = 2.75b. z = 1.44c. z = –1.44d. z = 1.19e. z = 40.66

____ 20. Which of the following indicates the range of possible values for Pearson’s correlation coefficient, r? a. 0 < r < 1b. −1 < r < 1c. −1 ≤ r ≤ 1d. −1 ≤ r < 1e. −1 < r ≤ 1

____ 21. Of the following, which is true of Pearson’s correlation coefficient, r?

a. The value of r does not depend on the units of y and x.b. r = 0 indicates a perfect correlation between x and y. c. r cannot be less than 0 or greater than 1.d. The value of r depends on which of two variables is labeled x.e. r| | is greater than 1.0 unless the points on a scatterplot line up exactly.

____ 22. Which of the following indicates the range of possible values of the coefficient of determination, r2 ?

a. 0 ≤ r2 ≤ 1b. 0 < r2

c. −1 ≤ r2 ≤ 1d. −1 < r2 < 1e. −1 < r2 < 0

____ 23. A scatterplot showed a nonlinear relationship between y and an independent variable x. The x values were transformed using a square-root transformation, and a scatterplot of y versus x′ = x was approximately linear. The least squares regression line summarizing the relationship between y and x' was y8 = 24 − 3x′. What is the predicted value of y when x = 16?

a. −24b. 16c. 12d. 12e. 4

Name: ______________________ ID: A

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____ 24. Consider the following five scatterplots. All are drawn to the same scale on both the x and y axes. For which scatterplot is the relationship negative?

a. d.

b. e.

c.

____ 25. An airline reports that for a particular flight operating daily between Phoenix and Atlanta, the probability of an on-time arrival is 0.64. Give a relative frequency interpretation of this probability.

a. In the long run, 0.64% of the time this particular flight that flies between Phoenix and Atlanta will arrive on time.

b. In the long run, 36% of the time this particular flight that flies between Phoenix and Atlanta will arrive on time.

c. In the long run, 64% of the time this particular flight that flies between Phoenix and Atlanta will arrive on time.

d. In the long run, 64% of the time this particular flight that flies between Phoenix and Atlanta will not arrive on time.

e. In the long run, 64% of the time this particular flight that flies between Phoenix and Atlanta will arrive earlier than expected.

Name: ______________________ ID: A

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____ 26. The faces of a twelve-sided die are numbered with the numbers 1 through 12. If you roll this die 600 times, how many nines do you expect to roll?

a. about 67b. about 50c. about 60d. about 100e. none

____ 27. Suppose you want to estimate the probability that a patient will develop an infection while hospitalized at a particular hospital. In the past year, this hospital had 8,650 patients, and 812 of them developed an infection. What is the estimated probability that a patient at this hospital will develop an infection?

a. P the patient develops an infectionÊËÁÁ

ˆ¯̃̃ =

1

812

b. P the patient develops an infectionÊËÁÁ

ˆ¯̃̃ =

1

8, 650

c. P the patient develops an infectionÊËÁÁ

ˆ¯̃̃ =

812

8, 650

d. P the patient develops an infectionÊËÁÁ

ˆ¯̃̃ =

5, 738

8, 650

e. P the patient develops an infectionÊËÁÁ

ˆ¯̃̃ =

812

5, 738

____ 28. Suppose you want to estimate the probability that a randomly selected customer at a particular grocery store will pay by credit card. Over the past 3 months, 70,600 purchases were made, and 22,200 of them were paid for by credit card. What is the estimated probability that a randomly selected customer will pay by credit card?

a. 0.3144b. 0.5391c. 0.7233d. 0.8548e. 0.8633

Name: ______________________ ID: A

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____ 29. A deck of 52 cards is mixed well, and 5 cards are dealt. It can be shown that (disregarding the order in which the cards are dealt) there are 2,598,960 possible hands, of which only 4 hands are royal flushes. (A royal flush is a hand consisting of 10, J, Q, K, and A, all of the same suit).

What is the probability that a hand will be a royal flush?

a. 482.598,960

b. 42.598,960

c. 452

d.2,598,9562.598,960

e.(4)(52)

2.598,960

____ 30. Each of 400 people who purchased a Honda Civic was classified according to gender and whether the car purchased had a hybrid engine or not.

Hybrid Not HybridMale 50 150Female 125 75

Find P hybrid | maleÊËÁÁ

ˆ¯̃̃.

a. 75400

≈ 0.19

b. 50200

≈ 0.25

c. 50175

≈ 0.29

d. 150225

≈ 0.67

e. 175200

≈ 0.88

Name: ______________________ ID: A

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____ 31. U.S. Postal Service standards call for overnight delivery within a zone of about 60 miles for any first-class letter deposited by the last posted collection time. Two-day delivery is promised within a 600-mile zone, and three-day delivery is promised for distances over 600 miles. An accounting firm conducted an independent audit by “seeding” the mail with letters and recording on-time delivery rates for these letters. Suppose that the results of the study were as follows:

Letter Mailed To Number of Letters Mailed Number of Letters Arriving on Time

Los Angeles 650 525New York 550 415Washington, D.C. 450 405Nationwide 7,000 6,220

Use the given information to estimate the probability of an on-time delivery in New York.

a. 4056, 220

≈ 0.0651

b. 415550

≈ 0.7545

c. 4157, 000

≈ 0.0593

d. 5256, 220

≈ 0.0844

e. 4156, 220

≈ 0.0667

____ 32. Which of the following random variables are discrete?

I). the volume of a balloon in litersII). the number of helium atoms in a balloonII). the number of balloons at a birthday party

a. I onlyb. II onlyc. III onlyd. II and III onlye. I, II, and III

Name: ______________________ ID: A

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____ 33. Which of the following random variables are continuous?

I). the air pressure in an automobile tire (in pounds per square inch)II). the diameter of an automobile tire (in centimeters)III). the number of miles traveled by an automobile tire

a. I onlyb. I and III onlyc. II and III onlyd. I, II, and IIIe. None of the variables is continuous.

____ 34. A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for the following random variable.x = number of slips marked “1”

a. 0,1b. 0,1,2c. 2d. 0e. 1

____ 35. Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year’s graduates:

Size of donation $0 $10 $25 $50Proportion of calls

0.35 0.15 0.40 0.10

Consider the variable x = amount of donation for a person selected at random from the population of last year’s graduates of this university.What is P x ≤ 25( )?

a. 0.10b. 0.50c. 0.55d. 0.75e. 0.90

Name: ______________________ ID: A

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____ 36. Suppose x is a continuous random variable with the probability distribution shouwn below.

What probability is represented by the shaded area?

a. P 0 < x < 20( )b. P 20 < x < 50( )c. 1 −P 20 < x < 50( )d. P x > 50( )e. none of these

____ 37. A chemical supply company currently has in stock 100 pounds of a certain chemical, which it sells to customers in 5-pound lots. Let x = the number of lots ordered by a randomly chosen customer. The probability distribution of x is as follows:

x 2 3 4 5p(x) 0.1 0.4 0.2 0.3

Calculate the mean value of x.

a. 2.2b. 2.5c. 2.7d. 3.3e. 3.7

____ 38. Determine the area under the z curve to the right of –1.82

a. P z ≥ −1.82( ) = 0.0015b. P z ≥ −1.82( ) = 0.0344c. P z ≥ −1.82( ) = 0.9076d. P z ≥ −1.82( ) = 0.9656e. P z ≥ −1.82( ) = 0.9876

Name: ______________________ ID: A

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____ 39. A gasoline tank for a certain car is designed to hold 19 gallons of gas. Suppose that the random variable x = actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 19.0 gallons and standard deviation 0.2 gallon.

What is the probability that a randomly selected tank will hold at least 18.9 gallons?

a. 0.19b. 0.69c. 1d. 0.31e. 0.81

____ 40. Thirty-seven percent of the customers of a grocery store use an express checkout. Consider four randomly selected customers, and let x denote the number among the four who use the express checkout.

Calculate P x ≤ 2( ) .

a. 0.53b. 0.85c. 0.70d. 0.30e. 0.50

____ 41. A business has five customer service telephone lines. Let x denote the number of lines in use at any given time. Suppose that the probability distribution of x is as follows:

x 0 1 2 3 4 5p(x) 0.10 0.20 0.35 0.15 0.15 0.05

Find the standard deviation of x. Round your answer to two decimal places.

a. 2.5b. 1.33c. 0.98d. 1.22e. 1.25

Name: ______________________ ID: A

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____ 42. Consider the following two statistical inference situations:

I. A technician at a water-bottling facility wishes to test whether one of the filling machines is delivering less fluid per bottle than it is intended to deliver.

II. Another technician at this same facility wished to determine the number of milliliters of water being delivered per bottle for the filling machine in question.

Which of these inference situations are hypothesis testing problems?

a. I onlyb. II onlyc. both I and IId. neither I nor IIe. Situations such as I and II are not suitable for statistical inference.

____ 43. For which of the following experimental questions would you be most interested in the population proportion instead of the population mean?

a. At this university, how many minutes a day do students exercise?b. Do students at this university intend to seek work immediately after graduation?c. Is the GPA of statistics students at this university higher than the national average?d. What is the mean GPA of statistics students at this university?e. Do students at this university score higher than the national average on the Graduate

Record Examination (GRE)?

____ 44. Which of the following statements is a population proportion?

a. A state census reports that 54% of the state’s citizens owns at least one dog..b. Out of 50 randomly-selected individuals, 19 indicated that they snore during sleep.c. The mean lifetime of all cell phone batteries is 11.3 hours.d. For a randomly-selected group of 20 computers running the Ubuntu operating system,

the mean boot time was 28 seconds.e. None of these

____ 45. A random sample is to be selected from a population that has a proportion of successes p = 0.50. Determine the mean and standard deviation of the sampling distribution of p8 for the sample size n = 100.

a. mean: µp8 = 0.50; standard deviation: σ p8 = 0.05

b. mean: µp8 = 0.50; standard deviation: σ p8 = 0.075

c. mean: µp8 = 0.50; standard deviation: σ p8 = 0.041

d. mean: µp8 = 0.85; standard deviation: σ p8 = 0.48

e. mean: µp8 = 0.85; standard deviation: σ p8 = 0.048

Name: ______________________ ID: A

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____ 46. A sampling distribution of p8 can be regarded as approximately normal when what conditions are met?

a. n ≥ 30b. n ≥ 10c. np ≥ 5 and n 1 − pÊ

ËÁÁˆ¯̃̃ ≥ 5

d. n ≥ 5e. np ≥ 10 and n 1 − pÊ

ËÁÁˆ¯̃̃ ≥ 10

____ 47. Suppose that 8% of the customers of a cable television company watch the Jewelry Network channel at least once a week. The cable company does not know the actual proportion of all customers who watch the channel at least once a week and is trying to decide whether to replace this channel with a new local station. The company plans to take a random sample of 150 customers and to use p8 as an estimate of the population proportion.

Determine the standard deviation of p8

a. 0.022b. 0.006c. 2.400d. 0.070e. 0.041

____ 48. A random sample will be selected from the population of all adult residents of a particular city. The sample proportion p8 will be used to estimate p, the proportion of all adult residents who are registered to vote. For which of the following situations will the estimate tend to be closest to the actual value of p?

I. n = 210 and p = 0.6II. n = 200 and p = 0.6III. n = 200 and p = 0.7

a. I only b. II only c. III only d. II and II onlye. All three estimates will be equally close to the actual value of p.

____ 49. An unbiased statistic is one that

a. is closely approximated by a normal curve.b. has the smallest variance.c. is mound-shaped.d. is nearly symmetric.e. does not consistently tend to underestimate or to overestimate the value of a

population characteristic.

Name: ______________________ ID: A

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____ 50. To estimate the proportion of faculty at a state university who own a home, a random sample of faculty is selected. For which of the following combinations of n and p8 would it be appropriate to use the

confidence interval p8 ± z critical value( )p8 1 − p8ÊËÁÁÁ

ˆ¯˜̃̃

n to estimate the population proportion?

a. n = 20 and p8 = 0.4b. n = 40 and p8 = 0.75c. n = 100 and p8 = 0.05d. n = 150 and p8 = 0.05e. n = 200 and p8 = 0.96

____ 51. Chuck has decided to increase the size of the sample he uses to estimate a population proportion.

What is the effect on the width of the associated confidence interval?

a. The width of the confidence interval increases.b. The width of the confidence interval decreases.c. The width of the confidence interval is unchanged.d. There is not enough information to say.

____ 52. A 90% confidence interval for a population proportion calculated using data from a random sample of size n = 51 is (0.573, 0.787). Which of the following is the 95% confidence interval calculated from the same data?

a. (0.602, 0.758)b. (0.620, 0.740)c. (0.553, 0.807)d. (0.543, 0.817)e. (0.486, 0.874)

____ 53. A report states that the mean yearly salary offer for students graduating with accounting degrees in 2012 was $49,007. Suppose that a random sample of 60 accounting graduates at a large university who received job offers resulted in a mean offer of $49,800 and a standard deviation of $3,100. What hypotheses should be used to test whether the accounting graduates at this school are securing starting salaries greater than $49,007?

a. H 0 :µ = 49,007 versus Ha :µ > 49,007b. H 0 :µ = 49,007 versus Ha :µ < 49,007c. H 0 :µ = 49,007 versus Ha :µ ≠ 49,007d. H 0 :µ = 49,007 versus Ha :µ = 49,800e. H 0 :µ < 49,007 versus Ha :µ ≠ 49,007

Name: ______________________ ID: A

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____ 54. A technician wishes to examine the breaking pressures, in pounds per square inch, of three brands of adhesives. In this study, the adhesives are used to bond two identical squares of 1/2”-thick pieces of acrylic plastic face-on, and then the assembly is tensionally stressed until the bond fails.For each of the adhesive brands, the test is repeated for 50 trials.

How many treatments are involved in this study?

a. 3b. 1c. 50d. 150e. 2

____ 55. For a random sample from a skewed population, for which of the following sample sizes would the sampling distribution of x be closest to normal in shape?

a. n = 11b. n = 18c. n = 19d. n = 22e. n = 40

____ 56. What is the standard deviation of x for random samples of size 80 from a population with a mean of 48 and a standard deviation of 11?

a. 0.138b. 1.23c. 0.371d. 11e. 6.6

____ 57. Let µx represent the mean value of the x sampling distribution and µ represent the population mean. What can be done to reduce the difference between µx and µ?

a. increase the sample sizeb. decrease the sample sizec. decrease the population standard deviationd. increase the population standard deviatione. nothing, since µx = µ for any population distribution.

Name: ______________________ ID: A

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58. The pie chart below summarizes the results of a survey of 300 randomly selected students at a particular high school. The investigators asked about soft drink preferences at a local high school.

(a) How many out of the 300 students indicated a preference for Dr. Pepper?

(b) Write a few sentences summarizing the soft drink preference for this sample of students.

(c) Using the information in the pie chart above, sketch a relative frequency bar chart for these data.

59. Explain in your own words what a hypothesis test is.

60. Explain in your own words the distinction between a null and alternative hypothesis.

61. One criticism of reading comprehension tests is that while they may measure reading comprehension, they also measure other factors not related to reading comprehension. A reading comprehension (RC) test on a major college entrance exam provides short English prose passages, and the examinees answer a set of multiple-choice items about the passage. To see if particular items measure something other than RC, investigators gave the RC test without the reading passages to a random sample of psychology students. The investigators reasoned that if questions were measuring knowledge or memory rather than just RC, students would answer questions at a higher rate than chance (20%, since there were 5 choices for each question.)

Suppose that on one question, 30 out of 100 examinees answered the question correctly. Is this sufficient evidence that students are using more than just reading comprehension to answer this question? Test the relevant hypothesis using α = 0.05.

Name: ______________________ ID: A

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62. Consider sampling from a skewed population. As the sample size, n, increases, some characteristics of the sampling distribution of x change. Does an increasing sample size cause changes in the characteristics of the sampling distribution shown below? If so, specifically how does the sampling distribution change?

a) The mean of the sampling distribution of x

b) The standard deviation of the sampling distribution of x

c) The shape of the sampling distribution of x

63. A new species of sea crab has been discovered, and an experiment conducted to determine whether or not the animal can regulate its temperature. That the animal can maintain a body temperature different from the surroundings would be considered evidence of this regulating capability. Ten of these sea crabs were exposed to ambient temperatures of 24 degrees Celsius. Their body temperatures were measured with the results below:

24.33, 24.61, 24.67, 24.64, 24.42, 24.97, 25.23, 24.73, 24.90, 24.44

For purposes of this example, assume that it is reasonable to regard these 10 crabs as a random sample from the population of all crabs of this species.

a) Calculate an estimate of the population mean.

b) Construct and interpret a 99% confidence interval for µ.

c) Does it appear from these data that the crabs are able to regulate their body temperature? Provide statistical justification for your response.

64. One of the properties of Pearson's r is: "The value of r does not depend on which of the two variables is labeled as x." In your own words, what does this mean?

65. According to internal testing done by the HardCore Apple Company, the mean firmness of their apples, as measured on the Mohs hardness scale is 7.0, with a standard deviation of 0.3.

a) If the claim by Hardcore is true, what is the mean of the sampling distribution of x for samples of size n = 16?

b) If the claim by HardCore is true, what is the standard deviation of the sampling distribution of x for samples of size n = 16?

c) If the distribution of HardCore firmness is approximately normal, and their claim about the mean firmness is true, what is the probability that the mean firmness of a random sample of size n = 16 will be less than 6.9?

Name: ______________________ ID: A

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66. Reading comprehension is arguably the single most important skill a student possesses. To assess the current levels of reading comprehension in 3rd grade, 25 students were randomly selected from school district class lists and given a reading comprehension test. The distribution of their scores was approximately normal with a mean of 180 and a standard deviation of 20.12. Construct a 99% confidence interval for µ, the population mean.

67. The Environmental Protection Agency (EPA) is charged with monitoring the environment. One aspect of this is keeping track of "acid rain," a broad term describing the fall of water through an acidic atmosphere. Acidity is measured on the pH scale, where pure water has a pH of 7.0. Normal rain is slightly acidic because carbon dioxide dissolves into it, and thus has a pH of about 5.5. (A lower pH indicates greater acidity.) Suppose the EPA wishes to determine whether a particular area is subject to acid rain. Let µ denote the true average for pH in this area.

a) What is the appropriate null hypothesis?

b) What is the appropriate alternative hypothesis?

c) In your own words, distinguish between a Type I and a Type II error in this context.

68. In cities and towns on the borders between states there is a significant amount of flight across state lines to avoid high state taxes on gasoline. Some states (such as Iowa) have large rivers for borders and tolls to cross the bridges. Do these tolls impede traffic to other states to get cheaper gasoline? To test this hypothesis, an experimental Toll-Free Week will be instituted at the Farmington Bridge, where currently 50 cars per day drive out of the state. Let µ denote the true average number of border crossings per day at Farmington if there were no toll.

a) What is the appropriate null hypothesis?

b) What is the appropriate alternative hypothesis?

c) In your own words, distinguish between a Type I and a Type II error in this context.

69. Suppose that a study has been published linking arsenic, which is commonly found in tap water, to increased cancer rates. The study also stated that arsenic levels below 10 ppm could be considered harmless. Suppose that residents of Hacienda Heights, CA, are worried about the arsenic level in the local tap water.

a) What hypothesis should they test?

b) Describe a Type I and Type II error in this context.

Name: ______________________ ID: A

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____ 70. Twenty-five assembly-line workers participated in a study to investigate the relationship between experience and the amount of time required to complete an assembly task. Assembly time (in minutes) and number of months the worker had been employed on the assembly line were measured for each worker. The resulting data on y = time to complete assembly and x = number of months on the assembly line were used to produce the scatterplot and computer output below.

Predictor Coef SE Coef T PConstant 84.683 5.602 15.12 0.000x −0.30411 0.04963 −6.13 0.000

S = 9.79097 R-Sq = 62.0% R-Sq(adj) = 60.4%

Predict the average time required to complete the assembly for an employee with 125 months of experience.

a. 46.7 minb. 80.9 minc. 88.5 mind. 110.4 mine. 122.7 min