12. A jewelry supplier has a supply of earrings which are 40% platinum. A store owner orders five s
dr.two
Question
12. A jewelry supplier has a supply of earrings which are 40%
platinum. A store owner orders five sets of earrings from the
supplier. If the supplier selects the pairs of earrings at random,
what is the chance that the jewelry store gets exactly two sets of
platinum pairs?
A) 0.4320
B) 0.2880
C) 0.3456
D) 0.1920
13. A certain large manufacturing facility produces 20,000 parts each week. The manager of the facility estimates that about 1% of the parts they make are defective. What is the variance for the number of defective parts made each week?
A) 200
B) 198
C) 14.1
D) 138
14. If a baseball player's batting average is 0.340 (i.e., the probability of getting a hit each time at bat is 0.340), find the probability that the player will have a bad season and get at most 60 hits in 200 times at bat?
A) 38.3%
B) 11.7%
C) 36.9%
D) 13.1%
15. The average diameter of sand dollars on a certain island is 3.00 centimeters with a standard deviation of 0.80 centimeters. If 9 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 2.65 centimeters. Assume that the variable is normally distributed.
A) 0.597
B) 0.840
C) 0.403
D) 0.903
16. The mean weight of loads of rock is 49.0 tons with a standard deviation of 12.0 tons. If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 47.6 tons. Assume that the variable is normally distributed.
A) 13.68
B) 36.32
C) 63.68
D) 86.32
17. What is the value for for a 95% confidence interval when n = 18?
A) 7.564
B) 8.672
C) 9.390
D) 8.231
18. Find the values for and when = .05 and n = 12.
A) 3.816 and 21.920
B) 4.404 and 23.337
C) 4.575 and 19.675
D) 5.226 and 21.026
19. Identify the degree of confidence displayed in the confidence interval shown below.
A) 90%
B) 95%
C) 98%
D) 99%
Use the following to answer question 20:
A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65.
20. Find the P-value for the test.
A) 0.4332
B) 0.2734
C) 0.1325
D) 0.0668
21. Using the z table, find the critical value (or values) for an = 0.021 left-tailed test.
A) –2.03
B) –2.31
C) –1.01
D) –1.15
22. A recent survey of gasoline prices indicated that the national average was $4.098 per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $3.924 per gallon with a population standard deviation of $0.053. What critical value should be used to test the claim using a = 0.01?
A) 1.26
B) 2.33
C) –1.26
D) –2.33
23. Is the statement a valid null hypothesis?
A) Yes, this is a statement that compares a parameter to a value.
B) Yes, this is a statement that compares two parameters.
C) No, equalities are not permitted in a null hypothesis.
D) No, there is no parameter contained in this statement.
24. An field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at = 0.10, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?
Pine trees Spruce trees
Sample size 40 60
Mean trunk diameter, cm 51 47
Population variance 105 167
A) The data does not support the conclusion that the average pine tree trunks are larger because the test value 0.74 is less than than the critical value1.28.
B) The data supports the conclusion that the average pine tree trunks are larger because the test value 1.72 is greater than than the critical value 1.28.
C) The data supports the conclusion that the average pine tree trunks are larger because the test value 1.72 is greater than than the critical value 1.65.
D) The data does not support the conclusion that the average pine tree trunks are larger because the test value 27.21 is greater than than the critical value 1.65.
25. Given the variances of the two samples below, find the test value and the degrees of freedom that should be used in an F test.
Sample 1 Sample 2
Variance 6 12
Sample size 13 28
A) test value = 4.00; d.f.N. = 28 and d.f.D. = 13
B) test value = 0.50; d.f.N. = 27 and d.f.D. = 12
C) test value = 2.00; d.f.N. = 27 and d.f.D. = 12
D) test value = 1.41; d.f.N. = 28 and d.f.D. = 13
26. Test the significance of the correlation coefficient r at = 0.05 for the data below.
X values 60 65 74 82 89
Y values 83 91 97 106 114
A) Accept because 16.05 < 3.18
B) Reject because 16.37 > 3.18
C) Accept because 16.37 < 2.78
D) Reject because 16.05 > 2.78
27. If the equation for the regression line is y' = 5x + 8, then a value of x = –2 will result in a predicted value for y of
A) 8
B) –11
C) –2
D) 5
28. Compute the standard error of the estimate for the data below. Round to the thousandths place.
A) 0.745
B) 0.697
C) 0.389
D) 0.500
29. A researcher is comparing 6 groups to test if they have the same means. There are 62 data values altogether. The degrees of freedom for the Between (dfB) and the degrees of freedom for the Within (dfW) are
A) dfB = 56, dfW = 61
B) dfB = 5, dfW = 56
C) dfB = 5, dfW = 61
D) dfB = 6, dfW = 61
30. If there are 5 means to be compared, then how many possible different comparisons (such as compared to ) are there altogether?
A) 5
B) 10
C) 20
D) 25
Short Answers (8 points each): Please complete each question and answer completely. You do not have to show your calculations – but partial points will be awarded if parts of your calculations are correct.
1. Find the weighted mean for a particular student's scores on three exams if the first one was worth 75 points and the student received a score of 70%, the second was worth 50 points and the student received a score of 80%, and the third was worth 30 points and the student received a score of 95%?
2. A researcher has reason to believe that, for an experiment with 50 points, a 95% prediction interval would be of width 8. If the researcher wishes to run a more precise experiment that will result in a 95% prediction interval of width 4, then the researcher will require how many points?
3. Find and , if , , , and .
4. Joan has just moved into a new apartment and wants to purchase a new couch. To determine if there is a difference between the average prices of couches at two different stores, she collects the following data. Test the hypothesis that there is no difference in the average price. Use a = 0.05.
Store 1 Store 2
5. A quality control expert wants to estimate the proportion of defective components that are being manufactured by his company. A sample of 300 components showed that 20 were defective. How large a sample is needed to estimate the true proportion of defective components to within 2.5 percentage points with 99% confidence?
6. In a survey, 70% of the voters support a particular referendum. If 10 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.
7. Explain the difference between qualitative, quantitative, discrete, and continuous variables.
8. The dean of a local school wanted to determine if the grade distribution was independent of the subject matter taught. How many degrees of freedom does this contingency table have?
Subject A B C D E
Science 5 11 27 7 11
History 14 18 32 5 7
English 18 35 68 18 23
A) 0.4320
B) 0.2880
C) 0.3456
D) 0.1920
13. A certain large manufacturing facility produces 20,000 parts each week. The manager of the facility estimates that about 1% of the parts they make are defective. What is the variance for the number of defective parts made each week?
A) 200
B) 198
C) 14.1
D) 138
14. If a baseball player's batting average is 0.340 (i.e., the probability of getting a hit each time at bat is 0.340), find the probability that the player will have a bad season and get at most 60 hits in 200 times at bat?
A) 38.3%
B) 11.7%
C) 36.9%
D) 13.1%
15. The average diameter of sand dollars on a certain island is 3.00 centimeters with a standard deviation of 0.80 centimeters. If 9 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 2.65 centimeters. Assume that the variable is normally distributed.
A) 0.597
B) 0.840
C) 0.403
D) 0.903
16. The mean weight of loads of rock is 49.0 tons with a standard deviation of 12.0 tons. If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 47.6 tons. Assume that the variable is normally distributed.
A) 13.68
B) 36.32
C) 63.68
D) 86.32
17. What is the value for for a 95% confidence interval when n = 18?
A) 7.564
B) 8.672
C) 9.390
D) 8.231
18. Find the values for and when = .05 and n = 12.
A) 3.816 and 21.920
B) 4.404 and 23.337
C) 4.575 and 19.675
D) 5.226 and 21.026
19. Identify the degree of confidence displayed in the confidence interval shown below.
A) 90%
B) 95%
C) 98%
D) 99%
Use the following to answer question 20:
A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65.
20. Find the P-value for the test.
A) 0.4332
B) 0.2734
C) 0.1325
D) 0.0668
21. Using the z table, find the critical value (or values) for an = 0.021 left-tailed test.
A) –2.03
B) –2.31
C) –1.01
D) –1.15
22. A recent survey of gasoline prices indicated that the national average was $4.098 per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $3.924 per gallon with a population standard deviation of $0.053. What critical value should be used to test the claim using a = 0.01?
A) 1.26
B) 2.33
C) –1.26
D) –2.33
23. Is the statement a valid null hypothesis?
A) Yes, this is a statement that compares a parameter to a value.
B) Yes, this is a statement that compares two parameters.
C) No, equalities are not permitted in a null hypothesis.
D) No, there is no parameter contained in this statement.
24. An field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at = 0.10, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?
Pine trees Spruce trees
Sample size 40 60
Mean trunk diameter, cm 51 47
Population variance 105 167
A) The data does not support the conclusion that the average pine tree trunks are larger because the test value 0.74 is less than than the critical value1.28.
B) The data supports the conclusion that the average pine tree trunks are larger because the test value 1.72 is greater than than the critical value 1.28.
C) The data supports the conclusion that the average pine tree trunks are larger because the test value 1.72 is greater than than the critical value 1.65.
D) The data does not support the conclusion that the average pine tree trunks are larger because the test value 27.21 is greater than than the critical value 1.65.
25. Given the variances of the two samples below, find the test value and the degrees of freedom that should be used in an F test.
Sample 1 Sample 2
Variance 6 12
Sample size 13 28
A) test value = 4.00; d.f.N. = 28 and d.f.D. = 13
B) test value = 0.50; d.f.N. = 27 and d.f.D. = 12
C) test value = 2.00; d.f.N. = 27 and d.f.D. = 12
D) test value = 1.41; d.f.N. = 28 and d.f.D. = 13
26. Test the significance of the correlation coefficient r at = 0.05 for the data below.
X values 60 65 74 82 89
Y values 83 91 97 106 114
A) Accept because 16.05 < 3.18
B) Reject because 16.37 > 3.18
C) Accept because 16.37 < 2.78
D) Reject because 16.05 > 2.78
27. If the equation for the regression line is y' = 5x + 8, then a value of x = –2 will result in a predicted value for y of
A) 8
B) –11
C) –2
D) 5
28. Compute the standard error of the estimate for the data below. Round to the thousandths place.
A) 0.745
B) 0.697
C) 0.389
D) 0.500
29. A researcher is comparing 6 groups to test if they have the same means. There are 62 data values altogether. The degrees of freedom for the Between (dfB) and the degrees of freedom for the Within (dfW) are
A) dfB = 56, dfW = 61
B) dfB = 5, dfW = 56
C) dfB = 5, dfW = 61
D) dfB = 6, dfW = 61
30. If there are 5 means to be compared, then how many possible different comparisons (such as compared to ) are there altogether?
A) 5
B) 10
C) 20
D) 25
Short Answers (8 points each): Please complete each question and answer completely. You do not have to show your calculations – but partial points will be awarded if parts of your calculations are correct.
1. Find the weighted mean for a particular student's scores on three exams if the first one was worth 75 points and the student received a score of 70%, the second was worth 50 points and the student received a score of 80%, and the third was worth 30 points and the student received a score of 95%?
2. A researcher has reason to believe that, for an experiment with 50 points, a 95% prediction interval would be of width 8. If the researcher wishes to run a more precise experiment that will result in a 95% prediction interval of width 4, then the researcher will require how many points?
3. Find and , if , , , and .
4. Joan has just moved into a new apartment and wants to purchase a new couch. To determine if there is a difference between the average prices of couches at two different stores, she collects the following data. Test the hypothesis that there is no difference in the average price. Use a = 0.05.
Store 1 Store 2
5. A quality control expert wants to estimate the proportion of defective components that are being manufactured by his company. A sample of 300 components showed that 20 were defective. How large a sample is needed to estimate the true proportion of defective components to within 2.5 percentage points with 99% confidence?
6. In a survey, 70% of the voters support a particular referendum. If 10 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.
7. Explain the difference between qualitative, quantitative, discrete, and continuous variables.
8. The dean of a local school wanted to determine if the grade distribution was independent of the subject matter taught. How many degrees of freedom does this contingency table have?
Subject A B C D E
Science 5 11 27 7 11
History 14 18 32 5 7
English 18 35 68 18 23
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