Unformatted text preview:

Statistics 101 Final Exam December 20, 2004Notes:1. The exam is open book and notes. Calculators are permitted, but not computers.2. Please include all of your work in the blue book. 3. Please indicate the null and alternative hypotheses when appropriate. The questions on this exam are based on the operations of Wharton’s undergraduate placement office. The data are all simulated to protect confidentiality.1. (21 pts) Wharton School students who graduated in the class of 2005 were surveyed to obtain employment information. There were 625 graduates, but only 400 returned the survey. Sixty six respondents did not have a job at the time of the survey. The students without jobs were eliminated from the analysis of salary data. Summary data in units of thousands of dollars: Average salary=62.6; standard deviation=7.4; n=334. A. Are the salaries sufficiently high to make the claim that the mean salary µ exceeds 60? Use =.01B. i) If the true mean salary µ was really 61, what is the probability that the test in part A would incorrectly retain the null hypothesis? Assume that σ=7.4 ii) What sample size of salaries would be required so that the probability of incorrectly retaining the null hypothesis is .05 when the true mean is 61? Assume that σ=7.4 and =.01 C. One of the concerns of the study is that 225 graduates did not respond. Twenty of the non-respondents were called back and their salaries were recorded. These twenty non- respondents were matched (based on a variety of characteristics including major and location of job) to twenty from among the original 334 respondents. Summary data of the differences between the salaries of the original respondents and the respondents who provided salaries after they were called back: Average=3.25; standard deviation=7.15; n=20. Are these data sufficient in concluding that the mean salary of initial respondents is different from the mean salary of those who did not respond initially? Use =.052. (21 pts) Data were collected on the number of job offers that each of the initial 400 respondents received (See Figure 2a). Figure 2a Distribution of number of job offers-101234567891011.01 .05 .10 .25 .50 .75 . 90 . 95 .99-3 -2 -1 0 1 2 3Normal Quantile Plot100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%maximumquartilemedianquartileminimum 10.000 10.000 9.975 5.000 4.000 2.000 1.000 0.000 0.000 0.000 0.000QuantilesMeanStd DevStd Err Meanupper 95% Meanlower 95% MeanN 2.772.10789180.10539462.97719812.5628019 400MomentsJobsDistributionsA. i) If you were going to approximate the above data by a normal distribution what normal distribution would you use? ii) Use appropriate output to comment on whether a normal distribution is a reasonable description for the above data?B. i) What would be a 95% confidence interval for the mean assuming that =2.11? ii) What would be the required sample size so that the 95% confidence interval in Bi) has a margin of error of .2 jobs? Assume that =2.11Data are collected that relate whether a person did not receive any job or at least one job to choice of major (See Figure 2b).Figure 2b. Relationship between major and whether graduate received any job offerFreq: FrequencyJob?NoYes 14 3.50 9.52 21.21 30 7.50 21.74 45.45 7 1.75 19.44 10.61 15 3.75 18.99 22.73 133 33.25 90.48 39.82 108 27.00 78.26 32.34 29 7.25 80.56 8.68 64 16.00 81.01 19.16 66 16.50 334 83.50 147 36.75 138 34.50 36 9.00 79 19.75 400MajorCountTotal %Col %Row %Finance Management Marketing OtherContingency TableModelErrorC. TotalNSource 3 394 397 400DF 4.53140 504.30675 508.83816-LogLike0.0089RSquare (U)Likelihood RatioPearsonTest 9.063 8.523ChiSquare 0.0285 0.0364Prob>ChiSqTe stsContingency Analysis of Major By Job?C. Find a 95% confidence interval for the proportion of students who did not receive any job offer?D. i) Describe in one or two sentences how the fraction of students without jobs vary with respect to major. ii) The P-value of .0364 (labeled Prob>ChiSq in the Pearson row) is the P-value corresponding to the null hypothesis that there is no relationship between Major and whether a student does not receive any job offer. Explain what the P-value means in the context of this problem and how you would use this P-value in testing the null hypothesis.3. (20 pts) Assume that the number of job offers has the following probability distribution: x: 0 1 2 3 4 5 6 7 8 9 10 p(x): .15 .15 .25 .20 .11 .07 .02 .02 .01 .01 .01A. What is µ for this probability distribution?B. Determine whether the sample we observed plausibly comes from this distribution bytesting whether 66 respondents out of 400 without a job is sufficient in rejecting the null hypothesis that the true proportion is .15 Use =.05One thousand samples of size 400 are generated from the above distribution (see Figure 3). Figure 3 Distribution of averages of 400 from the above p(x)2.22.32.42.52.62.72.82.9.001 .01 .05.10 .25 .50 . 75 .90. 95 . 99 . 999-4 -3 -2 -1 0 1 2 3 4Normal Quantile PlotAverage 100.0%99.5%97.5%90.0%75.0%50.0%25.0%10.0%2.5%0.5%0.0%maximumquartilemedianquartileminimum 2.9200 2.8598 2.7749 2.7025 2.6375 2.5725 2.5025 2.4400 2.3850 2.3250 2.1575QuantilesMeanStd DevStd Err Meanupper 95% Meanlower 95% MeanN 2.570990.10081980.00318822.57724632.5647337 1000MomentsC. i) Explain whether or not the 1000 samples of averages is well-approximated by a normal distribution by referring to appropriate output. ii) The 95% confidence interval for the mean is obtained using the standard formula for each sample. Of these 1000 intervals 961 included the true mean. The null hypothesis is that the standard formula produces confidence intervals that include the mean 95% of the time. Would the null hypothesis be rejected at =.05? 4. (12 points) A regression is run relating number of job offers to salary. In Figure 4a all 400 individuals are included using a salary of zero for those who did not receive any offer.In Figure 4b the 66 respondents without a job


View Full Document

Penn STAT 101 - STAT 101 FINAL EXAM

Download STAT 101 FINAL EXAM
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view STAT 101 FINAL EXAM and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view STAT 101 FINAL EXAM 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?