,MATHEMATICS

Question 1 of 23

1.0 Points

image1.pngThe data presented in the table below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01 level of significance, is the proportion of seeds that germinate dependent on the seed type?

 

 

 

 

 

Seed Type

 

Observed Frequencies

 

Germinated

Failed to Germinate

1

31

7

2

57

33

3

87

60

4

52

44

5

10

19

image2.wmfA.Yes, because the test value 16.86 is greater than the critical value of 13.28

image3.wmfB.Yes, because the test value 16.86 is less than the critical value of 14.86

image4.wmfC.No, because the test value 16.86 is greater than the critical value of 13.28

image5.wmfD.No, because the test value 13.28 is less than the critical value of 16.86

image6.png Reset Selection

Question 2 of 23

1.0 Points

image7.pngThe chi-square goodness-of-fit test can be used to test for:

image8.wmfA.significance of sample statistics

image9.wmfB.normality

image10.wmfC.difference between population variances

image11.wmfD.difference between population means

image12.png Reset Selection

Part 2 of 16 –

Question 3 of 23

1.0 Points

image13.png

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars.

 

Store

1

2

3

4

5

6

Shelf Space

5

5

5

10

10

10

Weekly Sales

1.6

2.2

1.4

1.9

2.4

2.6

 

Store

7

8

9

10

11

12

Shelf Space

15

15

15

20

20

20

Weekly Sales

2.3

2.7

2.8

2.6

2.9

3.1

What is the estimated regression equation?

image14.wmfA.image15.png = 1.45 + 0.074x

image16.wmfB.image17.png = 2.63 – 0.174x

image18.wmfC.image19.png = 2.63 + 0.724x

image20.wmfD.image21.png = 1.45 + 0.724x

image22.png Reset Selection

Question 4 of 23

1.0 Points

image23.pngA single variable X can explain a large percentage of the variation in some other variable Y when the two variables are:

image24.wmfA.highly correlated

image25.wmfB.directly related

image26.wmfC.inversely related

image27.wmfD.mutually exclusive

image28.png Reset Selection

Question 5 of 23

1.0 Points

image29.png        Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx.  Using that data, find the estimated regression equation which can be used to estimate the monthly rent for apartments in this neighborhood using size as the predictor variable. Apartments.xlsx

image30.wmfA.    image31.png177.12 + 1.065(size)

image32.wmfB.image33.png177.12 + 0.8500(size)

image34.wmfC.image35.png1.065 + 177.12(size)

image36.wmfD.image37.png197.12 + 2.065(size)

image38.png Reset Selection

Part 3 of 16 –

Question 6 of 23

1.0 Points

image39.pngA pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men.  Assume α = 0.05.  What is the test value?

 

Women

Men

Sample size

50

80

Mean effect

7

6.95

Sample variance

3

4

image40.wmfA.t = 3.252

image41.wmfB.t = 0.151

image42.wmfC.z = 0.081

image43.wmfD.z = 0.455

image44.png Reset Selection

Question 7 of 23

1.0 Points

image45.pngMembers of the general adult population volunteer an average of 4.2 hours per week. A random sample of 20 female college students and 18 male college students produced the results given in the table below. At the .01 level of significance, is there sufficient evidence to conclude that a difference exists between the mean number of volunteer hours per week for male and female college students?

 

 

Females

Males

Sample size

20

18

Sample mean

3.8

2.5

Sample variance

3.5

2.2

image46.wmfA.No, because the test value 2.38 is greater than the critical value

image47.wmfB.No, because the test value 2.38 does not exceed the critical value

image48.wmfC.No, because the test value 2.90 is greater than the critical value

image49.wmfD.Yes, because the test value 2.90 is greater than the critical value

image50.png Reset Selection

Part 4 of 16 –

Question 8 of 23

1.0 Points

image51.pngA type II error occurs when:

image52.wmfA.the sample mean differs from the population mean

image53.wmfB.the null hypothesis is incorrectly accepted when it is false

image54.wmfC.the null hypothesis is incorrectly rejected when it is true

image55.wmfD.the test is biased

image56.png Reset Selection

Question 9 of 23

1.0 Points

image57.pngSuppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 7.7 seconds. What would you use for the alternative hypothesis?

image58.wmfA.H1: image59.png< 7.7 seconds

image60.wmfB.H1: image61.png7.7 seconds

image62.wmfC.H1: image63.png > 7.7 seconds

image64.wmfD.H1: image65.png = 7.7 seconds

image66.png Reset Selection

Question 10 of 23

1.0 Points

image67.pngIn an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7. State the null and alternative hypotheses.

image68.wmfA.H0: image69.png= 75, H1: image70.png > 75

image71.wmfB.H0: image72.png = 75, H1: image73.png ≠ 75

image74.wmfC.H0: image75.png image76.png 75, H1: image77.png > 75

image78.wmfD.H0: image79.png image80.png 75, H1: image81.png < 75

image82.png Reset Selection

Part 5 of 16 –

Question 11 of 23

1.0 Points

image83.pngA previous study of nickels showed that the standard deviation of the weight of nickels is 150 milligrams. How many nickels does a coin counter manufacturer need to weigh so that she can be 98% confident that her sample mean is within 25 milligrams of the true average weight of a nickel?

image84.wmfA.36

image85.wmfB.196

image86.wmfC.239

image87.wmfD.139

image88.png Reset Selection

Question 12 of 23

1.0 Points

image89.pngA sample of 23 European countries found that the variance of life expectancy was 7.3 years. What is the 95% confidence interval estimate for the variance of life expectancy in Europe?

image90.wmfA.27.2 < image91.png < 118.3

image92.wmfB.5.6 < image93.png< 10.3

image94.wmfC.4.4 < image95.png< 14.6

image96.wmfD.28.9 < image97.png< 115.0

image98.png Reset Selection

Part 6 of 16 –

Question 13 of 23

1.0 Points

image99.pngGiven that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 < X < 90) is

image100.wmfA.0.1915

image101.wmfB.0.1498

image102.wmfC.0.3413

image103.wmfD.0.5328

image104.png Reset Selection

Part 7 of 16 –

Question 14 of 23

1.0 Points

image105.pngSuppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30. What is the probability that between 25 and 30 batteries (inclusive) will last at least 8 hours?

image106.wmfA.0.7792

image107.wmfB.0.0839

image108.wmfC.0.1186

image109.wmfD.0.9169

image110.png Reset Selection

Part 8 of 16 –

Question 15 of 23

1.0 Points

image111.pngIf two events are independent, what is the probability that they both occur?

image112.wmfA.0.0

image113.wmfB.0.5

image114.wmfC.1.00

image115.wmfD.Cannot be determined from the information given

image116.png Reset Selection

Part 9 of 16 –

Question 16 of 23

3.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A sport preference poll yielded the following data for men and women. Use a 5% significance level and test to determine if sport preference and gender are independent.

Sport Preferences of Men and Women

 

Basketball

Football

Soccer

 

Men

20

25

30

75

Women

18

12

15

45

 

38

37

45

120

What is the test value for this hypothesis test? Answer:   image117.wmf

Round your answer to two decimal places. What is the critical value for this hypothesis test?  Answer:  image118.wmf

Round your answer to two decimal places. What is the conclusion for this hypothesis test?  Choose one. 1.  There is sufficient evidence to support the claim that one’s sport preference is dependent on one’s gender. 2. There is not sufficient evidence to support the claim that one’s sport preference is dependent on one’s gender. Answer:  image119.wmf

Enter only a 1 or 2 for your answer.

Part 10 of 16 –

Question 17 of 23

1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results:

Store

Shelf Space(X)

Weekly Sales(Y)

1

10

2.0

2

10

2.6

3

10

1.8

4

15

2.3

5

15

2.8

6

15

3.0

7

20

2.7

8

20

3.1

9

20

3.2

10

25

3.0

11

25

3.3

12

25

3.5

Find the equation of the regression line for these data.  What is the value of the standard error of the estimate?  Place your answer, rounded to 3 decimal places, in the blank.  Do not use a dollar sign.  For example, 0.345 would be a legitimate entry.  image120.wmf

 

Part 11 of 16 –

Question 18 of 23

1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. An investor wants to compare the risks associated with two different stocks. One way to measure the risk of a given stock is to measure the variation in the stock’s daily price changes. In an effort to test the claim that the variance in the daily stock price changes for stock 1 is different from the variance in the daily stock price changes for stock 2, the investor obtains a random sample of 21 daily price changes for stock 1 and 21 daily price changes for stock 2. The summary statistics associated with these samples are: n1 = 21, s1 = .848, n2 = 21, s2 = .529. If you follow Bluman’s advice and place the larger variance in the numerator when computing the test value, at the .05 level of significance, what is the critical value associated with this test of hypothesis? Place your answer, rounded to 2 decimal places, in the blank. For example, 3.45 would be a legitimate entry. image121.wmf

Part 12 of 16 –

Question 19 of 23

1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.

Place your answer, rounded to four decimal places, in the blank.   image122.wmf

When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.

Part 13 of 16 –

Question 20 of 23

1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. Senior management of a consulting services firm is concerned about a growing decline in the firm’s weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the management randomly selected a sample of size 51 from the available frame. The sample mean and sample standard deviations were 48.5 and 7.5 hours, respectively. Construct a 90% confidence interval for the standard deviation of the number of hours this firm’s employees spend on work-related activities in a typical week. Place your LOWER limit, in hours, rounded to 1 decimal place, in the first blank. For example, 6.7 would be a legitimate entry. image123.wmf

Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3 would be a legitimate entry. image124.wmf

Part 14 of 16 –

Question 21 of 23

1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that more than three of them will experience a bad side effect? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate answer.   image125.wmf

Part 15 of 16 –

Question 22 of 23

1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A statistician wishes to test the claim that the standard deviation of the weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 30 firemen and found s = 27.2 pounds. Assuming that the weights of firemen are normally distributed, if the statistician wanted to test her research hypothesis at the .05 level of significance, what is the critical value? Place your answer, rounded to 3 decimal places, in the blank. For example, 23.456 would be a legitimate entry. image126.wmf

Part 16 of 16 –

Question 23 of 23

1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A restaurant menu has a price-fixed complete dinner that consists of an appetizer, entrée, beverage, and dessert. You have a choice of five appetizers, ten entrees, three beverages, and six desserts. How many possible complete dinners are possible?

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