• Based on the sample data and a significance level equal to 0.05, does there appear to be a difference in the proportion of loan defaults between residential and commercial customers?
• Prepare a short response to the Vintner board of directors. Include in your report a graph of the data that supports your statistical analysis.
• Consider the outcome of the hypothesis test in part a. In the last five audits, 10 residential and 10 commercial customers were selected. In three of the audits, there were more residential than commercial loan defaults. Determine the probability of such an occurrence.
 t-Test: Two-Sample Assuming Equal Variances Residential Loan Status Commercial Loan Status Mean 1.155 1.180952 Variance 0.131633 0.149634 Observations 200 105 Pooled Variance 0.137812 Hypothesized Mean Difference 0 df 303 t Stat -0.58009 P(T<=t) one-tail 0.281143 t Critical one-tail 1.649898 P(T<=t) two-tail 0.562286 t Critical two-tail 1.967824

Q2The California State Highway Patrol recently conducted a study on a stretch of interstate highway south of San Francisco to determine what differences, if any, existed in driving speeds of cars licensed in California and cars licensed in Nevada. One of the issues to be examined was whether there was a diffrence in the variability of driving speeds between cars licensed in the two states. The data file Speed-Test contains speeds of 140 randomly selected California cars and 75 randomly selected Nevada cars. Based on these sample results, can you conclude at the 0.05 level of significance there is a difference between the variations in driving speeds for cars licensed in the two states?

 t-Test: Two-Sample Assuming Equal Variances California Cars Out-of-State Cars Mean 64.45 61.96 Variance 64.29245 59.76865 Observations 140 75 Pooled Variance 62.7208 Hypothesized Mean Difference 0 df 213 t Stat 2.197197 P(T<=t) one-tail 0.014542 t Critical one-tail 1.652039 P(T<=t) two-tail 0.029084 t Critical two-tail 1.971164

There is a difference between the two cars speed and thus it can be said that there is a significant difference in the two states.

Q3 The Ecco Company makes electronics products for distribution throughout the world. As a member of the quality department, you are interested in the warranty claims that are made by customers who have experienced problems with Ecco products. The file called Ecco contains data for a random sample of warranty claims. Large warranty claims not only cost the company money but also provide adverse publicity. The quality manager has asked you to provide her with a range of values that would represent the percentage of warranty claims filed for more than \$300. Provide this information for your quality manager.

 Sum of %total Column Labels Row Labels 1 2 3 4 Grand Total 1 0.20965 0.300377 0.146518 0.029564 0.686109 1 0.18429 0.195902 0.090594 0.01328 0.484067 2 0.008442 0.073476 0.044513 0.016283 0.142714 3 0.016917 0.030999 0.011412 0.059328 2 0.097534 0.106477 0.039274 0.023157 0.266442 1 0.090126 0.08719 0.006607 0.012813 0.196737 2 0.007408 0.019287 0.023091 0.049785 3 0.009577 0.010344 0.019921 3 0.010544 0.011278 0.025626 0.047449 1 0.017852 0.017852 2 0.010544 0.011278 0.007775 0.029597 Grand Total 0.317728 0.418132 0.211418 0.052721 1

Q4 The state transportation department recently conducted a study of motorists in Idaho. Two main factors of interest were whether the vehicle was insured with liability insurance and whether the driver was wearing a seat belt. A random sample of 100 cars was stopped at various locations throughout the state. The data are in the file called Liabins. The investigators were interested in determining whether seat belt status is independent of insurance status. Conduct the appropriate hypothesis test using a 0.05 level of significance and discuss your results.

 Driving Citations Vehicle Year Driver Sex Driver Age Seat Belt Status Law Knowledge Employment Status Year In State Registered Vehicles Years Education Insurance Certificate Status Insurance Status Driving Citations 1 Vehicle Year 0.030072 1 Driver Sex -0.25747 0.258334 1 Driver Age -0.29097 0.116277 0.041819 1 Seat Belt Status 0.009689 -0.22479 -0.11649 -0.1071 1 Law Knowledge -0.02023 -0.06389 -0.04404 0.164283 0.177074 1 Employment Status -0.1347 0.098752 0.192186 0.306856 -0.06546 0.186704 1 Year In State -0.17428 0.12232 -0.08811 0.610012 0.018003 0.022402 0.03915 1 Registered Vehicles -0.17653 -0.04777 -0.13674 0.330033 -0.09816 0.046213 0.011787 0.285945 1 Years Education -0.00536 0.247238 0.137123 0.048782 -0.28447 -0.22471 0.059279 0.055306 0.1084 1 Insurance Certificate Status 0.067598 -0.07084 -0.02452 -0.0343 -0.05786 0.080405 0.138235 -0.10396 -0.1895 0.102671 1 Insurance Status -0.00283 0.060221 -0.12737 0.046721 0.088611 -0.07135 0.042459 0.166711 0.149672 -0.01691 -0.14086 1

 SUMMARY OUTPUT Regression Statistics Multiple R 0.088611 R Square 0.007852 Adjusted R Square -0.00227 Standard Error 0.525144 Observations 100 ANOVA df SS MS F Significance F Regression 1 0.213886 0.213886 0.775578 0.380652 Residual 98 27.02611 0.275777 Total 99 27.24 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1.571429 0.198486 7.917078 3.81E-12 1.17754 1.965317 1.17754 1.965317 Insurance Status 0.18126 0.20582 0.880669 0.380652 -0.22718 0.589703 -0.22718 0.589703

Seat belt status is independent of insurance status

Q5 An economist for the state government of Mississippi recently collected the data contained in the file called Mississippi on the percentage of people unemployed in the state at randomly selected points in time over the past 25 years and the interest rate of Treasury bills offered by the federal government at that point in time.

• Develop a plot showing the relationship between the two variables.
• Describe the relationship as being either linear or curvilinear.
• Develop a simple linear regression model with unemployment rate as the dependent variable.
• Write a short report describing the model and indicating the important measures.

 SUMMARY OUTPUT Regression Statistics Multiple R 0.973125 R Square 0.946972 Adjusted R Square 0.943658 Standard Error 0.788972 Observations 18 ANOVA df SS MS F Significance F Regression 1 177.8604 177.8604 285.7299 1.26E-11 Residual 16 9.959637 0.622477 Total 17 187.82 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -19.3726 1.586889 -12.2079 1.6E-09 -22.7366 -16.0085 -22.7366 -16.0085 Interest Rates (x) 2.902579 0.171714 16.90355 1.26E-11 2.538561 3.266597 2.538561 3.266597

Linear