# devry math533 final exam

Question

1. (TCO A) Consider the following raw data, which is the result of selecting a random sample of 20 condominium sales in a particular development. The sale prices are given in thousands of dollars ($1,000s).

131 142 120 135 126

153 135 131 126 133

147 137 130 126 140

138 144 132 132 138

1a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on sale prices.

1b. In the context of this situation, interpret the Median, Q1, and Q3.

2. JR Trucking buys tires from three suppliers: Goodyear, Michelin, and Bridgestone. Data on the last 1,000 tires that were purchased are described in the table below.

Defective Not Defective Total

Goodyear 5 495 500

Michelin 6 294 300

Bridgestone 10 190 200

Total 21 979 1000

If you choose a tire at random, then find the probability that the tire

a. was made by Michelin.

b. was made by Goodyear and was defective.

c. was not defective, given that the tire was made by Bridgestone. (Points : 18)

3. (TCO B) DCW Chemical is planning to implement an acceptance sampling plan for raw materials. A random sample of 22 batches from a large shipment (having a large number of batches) is selected. If two or more of the 22 batches fail to meet specifications, then the entire shipment is returned. Otherwise, the shipment is accepted.

In a sample of 22 batches from a population that is 1% defective (1% of the batches fail to meet specifications), find the probability that

a. two or more batches fail to meet specifications.

b. exactly two batches fail to meet specifications.

c. fewer than two batches fail to meet specifications. (Points : 18)

4. (TCO B) Pharmacies continually monitor their prescription filling process. A local pharmacy has noted that the time to fill a prescription for a generic antibiotic is normally distributed with a mean of 9.3 minutes and a standard deviation of 1.8 minutes.

a. Find the probability that a prescription for a generic antibiotic takes less than 10 minutes to fill.

b. Find the probability that a prescription for a generic antibiotic takes between 7 and 9 minutes to fill.

c. The slowest 10% of prescription fills result in a special discount to the customer. How long must a prescription fill for a generic antibiotic take in order to qualify for this discount? (Points : 18)

5. (TCO C) An operations analyst from an airline company has been asked to develop a fairly accurate estimate of the mean refueling and baggage handling time at a foreign airport. A random sample of 36 refueling and baggage handling times yields the following results.

Sample Size = 36

Sample Mean = 24.2 minutes

Sample Standard Deviation = 4.2 minutes

a. Compute the 90% confidence interval for the population mean refueling and baggage time.

b. Interpret this interval.

c. How many refueling and baggage handling times should be sampled so that we may construct a 90% confidence interval with a sampling error of .5 minutes for the population mean refueling and baggage time? (Points : 18)

6. (TCO C) An auditor for the U.S. Postal Service wants to examine its special Two-Day Priority mail handling to determine the proportion of parcels that actually require longer than 2 days for delivery. A randomly selected sample of 100 such parcels is found to contain seven that required longer than 2 days for delivery.

a. Compute the 90% confidence interval for the population proportion of parcels that require longer than 2 days for delivery.

b. Interpret this confidence interval.

c. How large a sample size will need to be selected if we wish to have a 90% confidence interval that is accurate to within 1%? (Points : 18)

7. (TCO D) An auditor for the U.S. Postal Service wants to examine its special two-day priority mail handling to determine the proportion of parcels that actually arrive within the promised two-day period. A randomly selected sample of 1600 such parcels is found to contain 1250 that were delivered on time. Does the sample data provide evidence to conclude that the percentage of on-time parcels is more than 75% (using = .01)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.

d. Compute the test statistic.

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e. What does this mean?

g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does this sample data provide evidence (with = .01), that the percentage of on-time parcels is more than 75%? (Points : 24)

8. (TCO D) A manufacturer of athletic footwear claims that the mean life of his product will exceed 50 hours. A random sample of 36 shoes leads to the following results in terms of useful life.

Sample Size = 36 shoes

Sample Mean = 52.3 hours

Sample Standard Deviation = 9.6 hours

Does the sample data provide evidence to conclude that the manufacturer’s claim is correct (using = .10)? Use the hypothesis testing procedure outlined below..

a. Formulate the null and alternative hypotheses.

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.

d. Compute the test statistic.

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e. What does this mean?

g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does the sample data provide evidence to conclude that the manufacturer’s claim is correct (using = .10)? (Points : 24)

1. (TCO E) An airline plans to initiate service at an airport in a city of approximately 500,000 people. To determine staffing requirements, officials for the airline take advantage of the sample survey data on the relationship between the number of flights per week and the number of employees for 30 airlines at various airports in cities that are similar in size (approximately 300,000 to 700,000). The data is found below.

FLIGHTS EMP. PREDICT

104 88 50

89 71 150

94 85

63 40

49 24

48 22

42 23

50 24

21 6

70 45

75 54

80 70

85 72

40 18

35 12

30 10

25 8

28 7

35 12

42 18

56 32

65 42

72 50

81 60

91 68

98 79

104 80

81 58

77 58

72 52

Regression Analysis: EMP. versus FLIGHTS

The regression equation is

EMP. = – 23.3 + 1.04 FLIGHTS

Predictor Coef SE Coef T P

Constant -23.261 2.177 -10.68 0.000

FLIGHTS 1.04407 0.03202 32.60 0.000

S = 4.31057 R-Sq = 97.4% R-Sq(adj) = 97.3%

Analysis of Variance

Source DF SS MS F P

Regression 1 19752 19752 1063.00 0.000

Residual Error 28 520 19

Total 29 20272

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI

1 28.943 0.896 ( 27.107, 30.779) ( 19.924, 37.961)

2 133.350 2.883 (127.445, 139.255) (122.728, 143.973)XX

XX denotes a point that is an extreme outlier in the predictors.

Values of Predictors for New Observations

New Obs FLIGHTS

1 50

2 150

Correlations: FLIGHTS, EMP.

Pearson correlation of FLIGHTS and EMP. = 0.987

P-Value = 0.000

a. Analyze the above output to determine the regression equation.

b. Find and interpret in the context of this problem.

c. Find and interpret the coefficient of determination (r-squared).

d. Find and interpret coefficient of correlation.

e. Does the data provide significant evidence (= .05) that the number of flights can be used to predict the number of employees? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret.

f. Find the 95% prediction interval for the number of employees needed for an airline that has 50 flights per week. Interpret this interval.

g. Find the 95% confidence interval for the mean number of employees needed for airlines that have 50 flights per week. Interpret this interval.

h. What can we say about the number of employees needed for an airport that has 150 flights per week? (Points : 48)

1. (TCO E) The management of an international hotel chain is in the process of evaluating possible sites for a new hotel on a beach resort. As part of the analysis, management is interested in evaluating the relationship between the distance between a hotel and the beach, (Distance, X1 in miles), the number of golf courses on the premises (Golf, X2), and the average occupancy rate (Rate, Y as a %). A sample of 14 existing resort hotels is selected yielding the following results.

Distance Golf Rate

0.1 2 92

0.1 2 95

0.2 3 96

0.3 3 90

0.4 3 89

0.4 2 86

0.5 2 90

0.6 1 83

0.7 1 85

0.7 1 80

0.8 0 78

0.8 0 76

0.9 0 72

0.9 0 75

Correlations: Distance, Golf, Rate

Distance Golf

Golf -0.859

0.000

Rate -0.944 0.895

0.037 0.982

Cell Contents: Pearson correlation

P-Value

Regression Analysis: Rate versus Distance, Golf

The regression equation is

Rate = 91.3 – 18.0 Distance + 2.13 Golf.

Predictor Coef SE Coef T P

Constant 91.262 3.924 23.26 0.000

Distance -18.013 4.561 -3.95 0.002

Golf 2.132 1.119 1.91 0.083

S = 2.39278 R-Sq = 91.8% R-Sq(adj) = 90.3%

Analysis of Variance

Source DF SS MS F P

Regression 2 701.38 350.69 61.25 0.000

Residual Error 11 62.98 5.73

Total 13 764.36

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI

1 86.518 0.832 (84.688, 88.349) (80.943, 92.094)

Values of Predictors for New Observations

New Obs Distance Golf

1 0.500 2.00

a. Analyze the above output to determine the multiple regression equation.

b. Find and interpret the multiple index of determination (R-Sq).

c. Perform the multiple regression t-tests on , (use two tailed test with (= .10). Interpret your results.

d. Predict the average occupancy rate for a single hotel that is .5 miles from the beach and has two golf courses on the premises. Use both a point estimate and the appropriate interval estimate. (Points : 31)

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