ADM2304X Assignment#1 Spring-Summer 2016
ADM2304X Assignment#1 Spring-Summer 2016Dr. Suren Phansalker Telfer School of Management University of Ottawa1ADM2304XAssignment#1Prof.: Dr. Suren PhansalkerDue Date and Time: Sunday, May 29, 2016, Before 23:59 hrsPossibility of Late ‘Upload’ with penalty ends on Tuesday, May 31, 2015 at 23:59 hrs.Instructions:1. Before you upload your Assignment, you must convert your document to a ‘.pdf’ format. Documents not inthis format will lose marks and may not even be marked.2. You must use MiniTab for any required calculations. You must do the required calculations manually whenspecifically instructed to do so. You may cut and paste your MiniTab output on your assignment. However,such MiniTab output does not replace any of the steps specified in (3).3. When performing a hypothesis test, you must state the null and alternate hypotheses (S1), calculated value ofthe test statistic (S2), the level of significance and the critical value (S3), and your decision to reject or not toreject the null hypothesis based on the critical value (S4) and/or the p-value (S5), and your conclusion inmanagerial terms.4. If the level of significance, LS, is not specified, then assume it is 5%.5. You must attach your Integrity Statement to the assignment.Qu.#1 (35 marks)In the Content section of ADM2304X folder on BBLearn, two files(Assign#1_ADM2304X_SS16.MTW and Assign#1_ADM2304X_SS16.MTP) have beenposted with identical data on Body Mass Index (BMI) of all adult females in a certainsmall town. Use the file which your version of MiniTab can use properly. This(Assign#1_ADM2304X_SS16.pdf) is the third file with all the questions.Treat the set of data in Column1 as the population, and then use MniTab to obtain thepopulation mean and standard deviation of the population BMI.a. Is the population data reasonably normal? Justify your answer. From here on,assume that population standard deviation is not known.b. If the BMI is 32.00 or more, it is claimed that the health of the person couldbe at serious risk because of high level of obesity. Use MiniTab (Data MenuCode-Numericto Numeric) to code the data in Column1 and put it Column2, andname it ‘H_Obese’. When coding the BMI data in Column1 to Column2, use31.999 and below as ‘0’ and 32.000 and above as ‘1’. Find the populationproportion of highly obese males with data in Column2 by using MiniTab.c. In Column4, a simple random sample, called “Sample1” of size 100, has alreadybeen drawn from Column2. Calculate manually and find a 95% symmetricconfidence interval of the population proportion for this “Sample1” and confirm itwith MiniTab.d. Now use MiniTab ( Calc Menu-Random-Sample from Column- to Column) anddraw 19 additional samples of size n = 100 from the ‘H_Obese’ column orColumn2. The procedure must be repeated 19 times. Put these 19 additionalsamples in Column5 to Column23. Name these various samples as Sample2,Sample3, …, and Sample20. For each of these additional 19 samples, find the95% confidence interval for the population proportion by using MiniTab.e. Now examine the number of confidence intervals for the population proportionin all these 20 samples. Is this what you should expect? Justify your answer withdoing the appropriate count.ADM2304X Assignment#1 Spring-Summer 2016Dr. Suren Phansalker Telfer School of Management University of Ottawa2f. Calculate the probability of the exact number of Confidence Intervals youobtained from among the 20 which you found above in part ‘e’, and whichcontained the population proportion in your experiment.Qu.#2 (35 marks)a. For Sample1, manually test the hypothesis that the population proportion of’H_Obese’ people is not 17.5%. Also calculate the p-Value.b. Calculate the appropriate 95% Confidence Interval. Explain what it means.Explain if it is consistent with the conclusion you reached in part ‘a’ above.c. Confirm your results in part ‘a’ above with MiniTab. Is your conclusion in part ‘a’supported by the MiniTab output? Explain how that is so.d. What sample size should you use if you wanted your 95% confidence interval tohave a margin of error of ±4%?e. Now test the hypothesis that population proportion of ‘H_Obese’ people is lessthan 36%.f. Calculate the appropriate asymmetrical confidence interval or bound and explainif it is consistent with your conclusion in part ‘e’ above.Qu.#3 (10 marks)In newly designed and fabricated computer microprocessor chips, 2.5% of the chipscould be defective. In a sample of 50 such microprocessors, it is found that 4microprocessors are defective. Does this indicate that the true population proportion ofdefective microprocessor chips is more than 3%? (Hint: Calculate the p-Value to reachyour conclusion).Caveat: Do not simply use any approximation indiscriminately.Qu.#4 (20 marks)In a large city, two independent samples were taken for the BMI of males and femalesand by using BMI of 32 as the criterion (as in Question#1), the following data table wasobtained.Males FemalesObese: 25 48Total: 125 150a. Test the hypothesis that the proportion of obese males and obese females is thesame. You must use the ‘p-Value’ approach. What would be your conclusion if:i. Your Level of Significance (LS) is 5%.ii. Your LS is 1%.iii. Based on your observations in ‘i’ and ‘ii’ above, can you generalize yourfindings.b. Find a 95 Confidence Interval and specify if it is consistent with the conclusionyou reached in part ‘a’ with an LS of 5%. ADM2304X Assignment#1 Spring-Summer 2016Dr. Suren Phansalker Telfer School of Management University of Ottawa3c. Now test if the proportion of obese females is more than obese males. You mustuse the ‘critical value’ approach with a level of significance of 5%.d. Calculate the appropriate (asymmetric) 95% Confidence Interval and justify if itis consistent with your conclusion reached in part ‘c’.
