.494px;=”” block;=””>1. (TCO A) Consider the following data on the number of passengers on flight #231, which flies from
Chicago to Charlotte. A random sample of 20 such flights is selected with the number of passengers
noted below.
247
245 245
252 245
248 252
247 258
251 255
245 258
252 244
242 242
237 238
260 a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the
above sample data on number of passengers.
b. In the context of this situation, interpret the Median, Q1, and Q3.
(Points : 33)
2. Consider the following data on newly hired entry-level employees in relation to how many previous
positions they have held and which part of the country they were born.
0 1 2 3 or more Total East 3 5 2 1 11 Midwest 7 9 2 0 18 West 1 7 8 5 21 11 21 12 6 50 Total If you choose one person at random, then find the probability that the person
a. had 0 previous positions.
b. is from the West and had three or more previous positions.
c. had only one previous position, given that the person is from the Midwest. (Points : 18)
3. (TCO B) Welldale County officials claim that only 20% of homeowners are delinquent in the payment
of property taxes. An investigative reporter selects a random sample of 25 homeowners in Welldale
County. Assuming the officials are correct, find the probability that
a. at least 10 homeowners are delinquent in payment of property taxes.
b. fewer than five homeowners are delinquent in payment of property taxes.
c. exactly four homeowners are delinquent in payment of property taxes. (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
13.3 minutes and a standard deviation of 2.8 minutes.
a. Find the probability that a prescription for a generic antibiotic takes at least 10 minutes to fill.
b. Find the probability that the prescription for a generic antibiotic takes between 12 and 15 minutes to
fill.
c. The slowest 20% 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) 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 = 1.5 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) 6. (TCO C) A clock company is concerned about errors in assembly in their custom made clocks. A
simple random sample of 120 clocks yields nine clocks with errors in assembly.
a. Compute the 99% confidence interval for the proportion of clocks with errors in assembly.
b. Interpret this confidence interval.
c. How large a sample size will need to be selected if we wish to have a 99% confidence interval that is
accurate to within 1.5%? (Points : 18)
7. (TCO D) An investigative reporter selects a random sample of 100 lawnmower repair shops and asks
them to repair a particular brand of lawnmower. In only 36 of the cases the repair is done properly.
Does the sample data provide evidence to conclude that less than 40% of all lawnmower repairs shops
would repair this brand of lawnmower properly (with = .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 less than 40% of all lawnmower repairs
shops would repair this brand of lawnmower properly (with = .10)? (Points : 24)
8. (TCO D) Engineering studies show that it is feasible to install a windmill for generating electrical
power if the mean wind speed is greater than 14 mi per hour (mph). The Piedmont Electric Co-op is
considering locating mulls at the top of Mount Hunter. A random sample of 45 wind speed readings
yields the following results.
Sample Size = 45
Sample Mean = 14.9 mph
Sample Standard Deviation = 3.8 mph
Does the sample data provide sufficient evidence to conclude that installation is feasible at this
location (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 sufficient evidence to conclude that installation is feasible at this
location (using = .10)? (Points : 24) 1. (TCO E) At an auction, a national car rental agency sold 12 comparably equipped 3-year-old Chevrolet Corsicas. The data on mileage (X) and selling price (Y) are found below.
PRICE MILEAGE PREDICT 7000 60000 54000 8500 52000 80000 7000 62000 8900 48000 7600 55000 7200 60000 8500 50000 7800 53000 7200 58000 9000 48000 7200 60000 7700 55000 Correlations: PRICE, Mileage Pearson correlation of PRICE and Mileage = 0.970
PValue = 0.000 Regression Analysis: PRICE versus Mileage The regression equation is
PRICE = 15809 0.145 Mileage Predictor Coef SE Coef T P
Constant 15809.0 635.2 24.89 0.000
Mileage 0.14540 0.01149 12.66 0.000 S = 188.396 RSq = 94.1% RSq(adj) = 93.5% Analysis of Variance Source DF SS MS F P
Regression 1 5685070 5685070 160.17 0.000
Residual Error 10 354930 35493
Total 11 6040000 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 7957.5 55.8 (7833.2, 8081.8) (7519.7, 8395.3) 2 4177.2 291.4 (3527.9, 4826.4) (3404.1, 4950.3)XX XX denotes a point that is an extreme outlier in the predictors. Values of Predictors for New Observations New Obs Mileage 1 54000 2 80000 a. Analyze the above output to determine the regression equation.
b. Find and interpret ??1in 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 mileage can be used to predict the
price? 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 of 3-year-old Chevy Corsicas that have 54,000 in
mileage. Interpret this interval.
g. Find the 95% prediction interval for the price of a single 3-year-old Chevy Corsica that has 54,000 in
mileage. Interpret this interval. .
h. What can we say about the price for a 3-year-old Chevy Corsica that has 80,000 in mileage? (Points :
48)
1. (TCO E) A sample of 15 computers reveals the following data in years of service (X1, YEARS),
whether the computer is a MAC or not (X2, 1=Mac computer, 0=not a Mac computer), and the total
number of breakdowns (Y, BREAKDOWNS). The results are found below.
YEARS MAC BREAKDOWNS 1 1 0 1 0 1 2 1 0 2 0 2 2 1 1 2 0 3 3 1 1 3 0 4 4 1 2 4 0 5 4 0 6 5 1 3 5 0 7 6 0 8 Correlations: YEARS, MAC, BREAKDOWNS YEARS MAC
MAC 0.168 0.549 BREAKDOWNS 0.810 0.664 0.000 0.007 Cell Contents: Pearson correlation PValue Regression Analysis: BREAKDOWNS versus YEARS, MAC The regression equation is
BREAKDOWNS = 0.462 + 1.19 YEARS 2.68 MAC. Predictor Coef SE Coef T P
Constant 0.4625 0.4456 1.04 0.320
YEARS 1.1946 0.1169 10.22 0.000
MAC 2.6805 0.3470 7.72 0.000 S = 0.649016 RSq = 94.2% RSq(adj) = 93.3% Analysis of Variance Source DF SS MS F P
Regression 2 82.679 41.339 98.14 0.000
Residual Error 12 5.055 0.421
Total 14 87.733 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 3.755 0.367 (2.956, 4.554) (2.131, 5.379) Values of Predictors for New Observations New Obs YEARS MAC 1 5.00 1.00 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??1,??2 (use two tailed test with (= .10). Interpret your
results.
d. Predict the total number of breakdowns for a single computer that is a 5-year-old MAC. Use both a
point estimate and the appropriate interval estimate. (Points : 31)
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