# MATH 533 Final Exam

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**MATH 533 Final Exam **

**(TCO E) A newly developed low-pressure snow tire has been tested to see how it wears**…

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## MATH 533 Final Exam

MATH 533 Final Exam

**(TCO A) A random sample of 20 cars driving down I-294 is selected and their speed is monitored. The results are as follows (in mph).**

68 65 50 79 77 60 55

61 78 75

75 67 72 58 70 62 67

72 70 74

a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on speed per car.

b. In the context of this situation, interpret the Median, Q1, and Q3. (Points: 33)

**(TCO B) Consider the following data on newly hired employees in relation to which part of the country they were born and their highest degree attained.**

| | HS | BS | MS | PHD | Total |

East | | 3 | 5 | 2 | 1 | 11 |

Midwest | | 7 | 9 | 2 | 0 | 18 |

South | | 5 | 8 | 6 | 2 | 21 |

West | | 1 | 7 | 8 | 6 | 22 |

| Total | 16 | 29 | 18 | 9 | 72 |

Of you choose one person at random, then find the probability that the person

a. Has a PHD

b. is from the East and has a BS as the highest degree arraigned

c. has only a HS degree, given that person is from the West. (Points: 18)

**(TCO B) Midwest Airlines has had an 80% on time departure rate. A random sample of 20 flights is selected. Find the probability that**

a. exactly 15 flights depart on time in the sample

b. at least 17 flights depart on time in the sample

c. less than 11 flights depart on time in the sample. (Points: 18)

**(TCO B) The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls. The distribution of mean response times to fire calls follows a normal distribution with a mean of 12.8 minutes and a standard deviation of 3.7 minutes.**

**a. **Find the probability that a randomly selected response time is less than 15 minutes.

b. Find the probability that a randomly selected response time is less than 13 minutes.

c. The fastest 20% of fire departments will be singled out for a special safety award. How fast must a fire department be I order to qualify for the special safety award? (Points: 18)

**(TCO C) A transportation company wants to estimate the average length of time goods are in transit across country. A random sample of 20 shipments yields the following results.**

Sample Size = 20

Sample Mean = 4.6 days

Sample Standard Deviation = 1.50 days

a. Compute the 90% confidence interval for the population mean transit time.

b. Interpret this interval.

c. How many shipments should be sampled if we wish to generate a 99% confidence interval for the population mean transit time that is accurate to within .25 days? (Points: 18)

**(TCO C) United Express Delivery is interested in estimating the percentage of packages delivered damaged. A simple random sample of 500 packages yields 12 delivered damages and 488 delivered undamaged.**

**a. **Compute the 99% confidence interval for the population proportion of packages that are delivered damaged.

b. Interpret this confidence interval

c. How many packages should be sampled in to order to be 99% confident of being within .5% of the actual population proportion of packages delivered damaged? (Points: 18)

**(TCO D) A manager at Travis Savings and loan believes that less than 52% of their depositors won their homes. A random sample of 100 depositors is selected with the results that 46 depositors own their homes and the other 54 do not own their homes. Does the sample data provide evidence to conclude that less than 52% of all depositors at Travis Savings and Loan own their homes (with α = .05)? 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 less than 52% of all depositors at Travis Savings and Loan own their homes (with α = .05)? )Points: 24)

**(TCO D) Bill Smith is the Worthington Township manager. When citizens request a traffic light, the staff assesses the traffic flow at the requested intersection. Township policy requires the installation of a traffic light when an intersection averages more than 150 vehicles per hour. A random sample of 48 vehicles counts is done. The results are as follows:**

Sample Size = 48

Sample Mean = 158.3 vehicles/hr.

Sample Standard Deviation = 27.6 vehicles/hr.

Does the sample data provide evidence to conclude that the installation of the traffic light is warranted (using α = .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 norejection 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. Find the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does this sample data provide evidence (with α = 0.10), that the installation of the traffic light is warranted? (Points; 24)

MATH 533 Final Exam

**(TCO E) The management of JAL Airlines assumes a direct relationship between advertising expenditures and the number of passengers who choose to fly JAL. The following data is collected over the past 15 months of performance by JAL Airlines. Note that X=ADEXP (Advertising Expenditures in $1,000s), and Y=Passengers (number of passengers in 1,000s). The MINITAV printout can be found below.**

ADEXP | | PASSANGERS | | PREDICT |

100 | | 15 | | 120 |

120 | | 17 | | 250 |

80 | | 13 | | |

170 | | 23 | | |

100 | | 16 | | |

150 | | 21 | | |

100 | | 14 | | |

140 | | 20 | | |

190 | | 24 | | |

100 | | 17 | | |

110 | | 16 | | |

130 | | 18 | | |

160 | | 23 | | |

100 | | 15 | | |

120 | | 16 | | |

** 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 (α = .05) that advertising expenditures can be used to predict the number of passengers? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret.

f. Find the 95% confidence interval for the mean number of passengers when advertising expenditures were $120,000. Interpret this interval.

g. Find the 95% prediction interval for the number of passengers when advertising expenditures were $120,000. Interpret this interval.

h. What can we say about the number of passengers when advertising expenditures were $250,000? (Points : 48)

Prediction for PASSANGERS

**(TCO E) A newly developed low-pressure snow tire has been tested to see how it wears under normal dry weather conditions. Twenty of these tires were tested on standard passenger cars. These cars were driven at high speeds on a dry test track for varying lengths of time. We are interested in finding the relationship between hours driven (HOURS, X1), brand of car driven (BRAND, X2, where 0=Ford and 1 =General Motors), and tread wear (TREAD, Y in inches). The data is found below.**

Hours | Brand | Tread |

13 | 0 | 0.1 |

25 | 0 | 0.2 |

27 | 0 | 0.2 |

46 | 0 | 0.3 |

18 | 0 | 0.1 |

31 | 0 | 0.2 |

46 | 0 | 0.3 |

57 | 0 | 0.4 |

75 | 0 | 0.5 |

87 | 0 | 0.6 |

62 | 1 | 0.4 |

105 | 1 | 0.7 |

88 | 1 | 0.6 |

63 | 1 | 0.4 |

77 | 1 | 0.5 |

109 | 1 | 0.7 |

117 | 1 | 0.8 |

35 | 1 | 0.2 |

98 | 1 | 0.6 |

121 | 1 | 0.8 |

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 (α = .10). Interpret your results.

d. Predict the tread wear for tires from General Motors that were driven for 50 hours. Use both a point estimate and the appropriate interval estimate. (Points: 31)

MATH 533 Final Exam

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