Question 1. Seventeen salespeople reported the following number of sales calls completed last month.
72 93 82 81 82 97 102 107 119
86 88 91 83 93 73 100 102
a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on number of sales calls per month.
b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)Question 2.2. (TCO B) Consider the following data on new customers for AJ Auto Insurance, specifically the information of the risk level of the customer and the number of tickets they have had in the last year.
0 1 2 or more Total
Low Risk 56 22 8 86
Medium Risk 18 40 12 70
High Risk 11 13 20 44
Total 85 75 40 200
If you choose a customer at random, then find the probability that the customer
a. has zero tickets in the last year.
b. is high risk and had zero tickets in the last year.
c. has two or more tickets in the last year, given that the customer is high risk.
3. In a recent survey, 80% of the citizenry in a community favored the building of a municipal golf course. If you ask 15 citizens about this project, find the probability that
a. at least 9 favor the golf course project.
b. exactly 9 favor the golf course project.
c. less than 9 favor the golf course project.
4. Telcom is a telephone answering service for physicians. The length of a message is a normally distributed variable with a mean 152.3 seconds and a standard deviation of 22.8 seconds.
a. What percentage of messages lasts longer than 120 seconds?
b. What percentage of messages lasts between 90 and 120 seconds?
c. Find the 95th percentile for length of message (i.e., find the cutoff for the longest 5% of messages).
5. A tool manufacturing company wants to estimate the mean number of bolts produced per hour by a specific machine. A simple random sample of 9 hours of performance by this machine is selected and the number of bolts produced each hour is noted. This leads to the following results.
Sample Size = 9
Sample Mean = 62.3 bolts/hr
Sample Standard Deviation = 6.3 bolts/hr
a. Compute the 90% confidence interval for the average number bolts produced per hour.
b. Interpret this interval.
c. How many hours of performance by this machine should be selected in order to be 90% confident of being within 1 bolt/hr of the population mean number of bolts per hour by this specific machine? (Points : 18)
6. 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%?
7. For the past several years, at least 4% of the rooms were not cleaned by room service at the Holton Hotel by 3 p.m.
Customer satisfaction surveys have indicated that room availability before 3 p.m. would be a big plus for the hotel. Recently, the executive director took steps to reduce the proportion of rooms not cleaned by 3 p.m. A random sample of 1,400 rooms were selected over a 1-month period and 46 were found not cleaned by 3 p.m. Does the sample data provide evidence to conclude that the percentage of not cleaned rooms by 3 p.m. is less than 4% (with = .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 the percentage of not cleaned rooms by 3 p.m. is less than 4% (with = .05)?
8. The R. R. Bowker Company of New York collects information on the retail prices of collectible children's books and publishes its findings in Publisher's Weekly. Last year, the mean retail price of collectible children's books was $35.44. A random sample of 40 collectible children's books (published this year) is selected, the retail prices are noted, and the results are as follows:
Sample Size: 40
Sample mean: $38.75
Sample standard deviation: $7.35
Does the sample data provide evidence to conclude that the mean retail price of collectible children's books has increased over last year (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 this sample data provide evidence (with = 0.10), that the mean retail price of collectible children's books has increased over last year?
9. We consider the relationship between the age of a Fiat Aon, and its selling price. A sample of 16 used Fiat Aons is selected. The data is found below.
a. Analyze the above output to determine the regression equation.
b. Find and interpret B1 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 evidence ( = .05 ) that the age of a Fiat Aon can be used to predict the selling price of a Fiat Aon? 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 mean price for Fiat Aons that are 5 years old. Interpret this interval.
g. Find the 95% prediction interval for the price of a single Fiat Aon that is 5 years old. Interpret this interval.
h. What can we say about the price of Fiat Aons that are 10 years old?
10. A used car dealer is interested in determining the relationship between car mileage (i.e., the odometer reading, Miles X1, in 1,000s of miles), gender of the previous owner (Gender, X2 where 0=female and 1=male), and the trade value of the car (Value, Y in $100s). A random sample of 16 five-year-old cars of the same make, model, condition, and optional features is selected. The results are found below.
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 b1, b2 (use two tailed test with (= .10). Interpret your results.
d. Predict the trade value for a single car that 70,000 miles on the odometer and was owned by a male. Use both a point estimate and the appropriate interval estimate.