# Math 533- 64541

- (TCO A) Consider the following sample data on the age of the 30 employees that were laid off recently from DVC Inc.

21 38 20 26 37 52 37 24 45 20

50 49 44 30 29 42 56 46 60 30

32 25 47 55 38 25 20 29 32 30

- Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on age of employees being laid off.

- 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 |

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

a. is from the Midwest.

b. is from the South and has a PHD.

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

- (TCO B)A source in the Internal Revenue Service has stated that historically 90% of federal tax returns filed are free of arithmetic errors. A random sample of 25 returns are selected and checked carefully for arithmetic errors. Assuming independence, find the probability thata. all 25 returns are free of arithmetic errors.
b. at most 23 returns are free of arithmetic errors.

c. more than 17 are free of arithmetic errors. (Points : 18)

- (TCO B) The Bank of Connecticut issues Visa and Mastercard credit cards. The balances on these credit cards follow a normal distribution with a mean of $845 and standard deviation of $270.a. What percentage of balances is below $1,200?
b. What percentage of balances is between $600 and $1,000?

c. Find the 12th percentile for balance (i.e., find the cutoff for the lowest 12% of balances). (Points : 18)

Question 5.5. (TCO C) A large-sized bag of Neato Chips should contain 16 oz of potato chips. A sample of 50 large-sized bags is selected with the following results.
Sample Size = 50 Sample Mean = 15.85 oz Sample Standard Deviation = 1.53 oz a. Construct a 95% confidence interval for the mean amount of contents per bag. . b. Interpret this interval. c. How large a sample size will need to be selected if we wish to have a 99% confidence interval with a margin for error of .10 oz? (Points : 18)
6. (TCO C) The personnel manager of a large firm wants to find the percentage of employee absences that occur on Fridays. A random selection of 500 employee absences is taken from work records over the past several years. The data reveals that 220 of the 500 employee absences were on Fridays. a. Compute the 99% confidence interval for the population proportion of absences that are on Friday. 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 3%? (Points : 18)
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 90% of all orders are mailed within 72 hours (with a = .01)? (Points : 24)
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 a = .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 a = .10)? (Points : 24)
The regression equation is RETURN = 30.0 – 0.943 FOOTAGE Predictor Coef SE Coef T P Constant 29.976 1.238 24.22 0.000 FOOTAGE -0.94257 0.07921 -11.90 0.000 S = 0.969721 R-Sq = 91.0% R-Sq(adj) = 90.4% Analysis of Variance Source DF SS MS F P Regression 1 133.15 133.15 141.59 0.000 Residual Error 14 13.17 0.94 Total 15 146.31 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 15.838 0.244 (15.315, 16.360) (13.693, 17.982) 2 22.907 0.666 (21.479, 24.334) (20.384, 25.429)X X denotes a point that is an outlier in the predictors. Values of Predictors for New Observations New Obs FOOTAGE 1 15.0 2 7.5
Pearson correlation of RETURN and FOOTAGE = -0.954 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 (a = .05) that Footage can be used to predict Return? 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 rate of return on capital investment for malls that have square footage of 150,000. Interpret this interval. g. Find the 95% prediction interval for the rate of return on capital investment for a mall that has square footage of 150,000. Interpret this interval. h. What can we say about the rate of return on capital investment for a mall that has square footage of 75,000?
The regression equation is Y = 55.1 – 1.37 X1 + 8.05 X2 Predictor Coef SE Coef T P Constant 55.138 7.309 7.54 0.000 X1 -1.3736 0.4885 -2.81 0.020 X2 8.053 1.307 6.16 0.000 S = 6.07296 R-Sq = 93.1% R-Sq(adj) = 91.6% Analysis of Variance Source DF SS MS F P Regression 2 4490.3 2245.2 60.88 0.000 Residual Error 9 331.9 36.9 Total 11 4822.3 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 52.20 2.91 (45.62, 58.79) (36.97, 67.44) Values of Predictors for New Observations New Obs X1 X2 1 8.00 1.00
Y X1 X1 -0.800 0.002 X2 0.933 -0.660 0.000 0.020 Cell Contents: Pearson correlation P-Value 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 d. Predict the monthly premium for an individual having 8 years of driving experience and 1 driving violation during the past 3 years. Use both a point estimate and the appropriate interval estimate. (Points : 31) |