BP_Toront BP_Ottawa 134 104 121 114 109 119 126 124 136 105 132 99 126 123 122 102 124 103 125 101 118 120 134 110 115 116 102 110 140 110 118 115 96 113 116 132 122 137 136 101 119 102 111 117 104 106 108 119 119 130 128 121 132 128 141 Wt_Week0Wt_Week4 140 134 136 130 130 126 152 143 134 132 162 153 138 132 148 140 175 165 140 135 137 131 129 125 157 148 144 137 133 130 ADM 2304 Assignment 2 Due Date: Tuesday, March 1, 2016 at midnight. Instructions: 1. You may use Minitab or other software for any calculations. However, you must show your manual calculations when asked. You may paste your output onto your assignment to show your use of Minitab; however, this output does not replace any of the steps outlined below. This means that answers that are exclusively Minitab output may receive only one mark. 2. If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance (default value of 5% unless specified otherwise), the decision rule in terms of the critical value, the test statistic or p-value, your decision (whether to reject or not to reject the null hypothesis), and your conclusion written also as a managerial statement. These steps must be completed in addition to any Minitab output. 3. The data for this assignment can be found in Assign2_Data.mtw or Assign2_Data.xls. 4. Remember to include your integrity statement. Your assignment must be uploaded to Blackboard in pdf format. Question 1. [10 marks] Consider the data on the "systolic" blood pressure (the higher of the two blood pressure readings--the lower number being the "diastolic" pressure) for random samples of adult males living in Ottawa and Toronto, respectively. These data will be referred to simply as BP for blood pressure. a. To compare the two samples, is it better to use a parametric or a non-parametric test? Explain with reference to specific boxplots. b. Now use a parametric test at the 0.05 level of significance to determine if the mean BP of Toronto adult males is more than 2.5 higher than the mean BP of Ottawa adult males. Do the test manually, using the p-value approach and assume equal population variances. c. Show the manual calculation of the appropriate asymmetric (1-sided) confidence interval for the test above and explain how it is consistent with the conclusion above. d. What is the minimum value by which the mean BP is higher in Toronto than the mean BP in Ottawa? Question 2. [5 marks] Now suppose it was found that the 19th observation in the sample from Ottawa had a dataentry error. The value should have been 157 and not 137. a. Using the revised data, test whether the median BP of adult males in Toronto is higher by more than 2.5 than the median BP of adult males in Ottawa. b. Which of the two tests is more appropriate for the revised datathe parametric test or the nonparametric test? Explain with reference to specific boxplots. Question 3. [15 marks] A weight loss clinic claims that if clients follow their programme for 4 weeks, they will lose more than 5 lbs by the end of the programme. An independent evaluator obtained data to test the clinic's claim. 'Wt_Week0' is the weight in pounds of the client at the start of the programme and 'Wt_Week4' is the weight of the same client at the end of the 4 weeks. a. Explain whether the samples are independent or paired, based on the nature of the data. Now use Minitab to calculate the correlation coefficient between the two samples. Explain whether this supports your answer. b. Use an appropriate parametric test to determine whether the claim made by the clinic can be supported. Show your manual calculations. c. Calculate manually the appropriate asymmetric (1-sided) confidence interval for the mean weight loss and explain if it is consistent with your conclusion above. d. Now do a non-parametric test to determine if the population median weight loss is more than 5 lbs. e. Which test is more appropriate: the parametric or the non-parametric test? Explain with reference to appropriate boxplots. What numerical measures also support your choice? Question 4. [15 marks] A survey of randomly selected social media users was conducted to find out the number of users who use a given type of "Social Medium" as their first preference by their "Age Group". The various categories of the two variables are given the data table below. For example, "A1" refers to age group 15 to less than 20 years; and "M3" refers to "Twitter". The other categories are defined similarly. Use a 5% level of significance throughout this question. Age Group in Yrs A1:15- <20 a2:20- <30 a3:30- <40 a4:40- <65 a5:>=65 Total M1:E-mail 50 60 65 55 35 265 Social Media Used as a First Preference M2:FBook M3:Twitter M4: IGram M5: Other 45 50 25 27 55 50 30 30 45 30 25 25 30 20 15 26 45 35 15 17 220 185 110 125 Total 197 225 190 146 147 905 a. State the hypotheses to test whether the preferred choice of social media is related to the age group. Name the test you would perform. b. Calculate manually the "degrees of freedom" and do the calculations manually for the two cells (A1 & M1) and (A3 & M5). This means you must calculate manually E11, Chisquare11, E35 and Chisquare35. However, you may use Minitab to find the value of the test statistic. Complete the test using the critical value approach. What do you conclude? c. Explain how the p-value is found and state your conclusion. Is this conclusion consistent with the critical value approach? d. We define the pi's as the population proportions for the various Mi's. Test whether the population distribution of social media used by the age group A1 is consistent with the following: p1 = 25%, p2 = 25% and p4 = p5 = 10%, p3 = the rest. Use a 5% level of significance and the critical value approach