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# BUAD 310:HW5 Due on April 05, 2011 1. A recent repot concludes that while Internet users like the convenience of online shopping, they do have...

1. A recent repot concludes that while Internet users like the convenience of online shopping, they do have concernsabout privacy and security (Online Shopping,Washington, DC, Pew Internet & American Life Project, February2008). Respondents were asked to indicate their level of agreement with the statement I don't like giving mycredit card number or personal information online." The table gives a subset of responses. Test an appropriatehypothesis for the relationship between age and level of concern about privacy and secutrity online.Strongly Agree Agree Disagree Strongly Disagree TotalAges 18-29 127 147 138 10 422Ages 30-49 141 129 78 55 403Ages 50-64 178 102 64 51 395Ages 65 + 180 132 54 14 380Total 626 510 334 130 1600(a) Name the appropriate procedure.(b) State the null and alternative hypothesis.(c) State the test-statistic.(d) Assuming the null hypothesis is true, what is the sampling distribution of the test statistic?(e) Find the exact p-value of the test-statistic using Minitab.(f) Assuming the level of signicance = 5%, write down your conclusion and interpret it.2. For a lottery to be successful, the public must have condence in its fairness. One of the lotteries in Marylandis Pick-3 Lottery, where 3 random digits are drawn each day. A fair game depends on every value (0 to 9) beingequally likely at each of the three positions. If not, then someone detecting a pattern could take advantage ofthat and beat the lottery. To investigate the randomness, we'll look at data collected over a recent 32-weekperiod. Althought the winning numbers look like three digit numbers, in fact, each digit is a randomly drawn1numeral. We have 654 random digits in all. Are each of the digits from 0 to 9 equally likely? Here is a tableof the frequencies.Group Count %0 62 9.4801 55 8.4102 66 10.0923 64 9.7864 75 11.4685 57 8.7166 71 10.8567 74 11.3158 69 10.5509 61 9.327(a) Set up the relevant null and alternative hypothesis.(b) Write down the test statistic to be used for testing the hypothesis.(c) What is the sampling distribution of the test statistic if the null hypothesis is true?(d) If the level of signicance = 5%, write down the rejection region.(e) Based on the data, do you reject the null hypothesis? Justify.(f) Did you commit a type I error based on your conclusion to 2e above?3. Many people believe that the moon inuences the actions of some individuals. A study of dementia patients innursing homes recorded various types of disruptive behaviors every for 12 weeks. For each patient the averagenumber of disruptive behaviors was computed for moon days and for all other days. The data for 10 randomlychosen subjects whose behaviors were classied as aggressive are presented in the table below. It is desired totest whether the average number of disruptive behaviors is dierent on full moon days as compared to otherdays.2Patient Full moon days Other days1 3.33 0.272 3.67 0.593 2.67 0.324 3.33 0.195 3.33 1.266 3.67 0.117 4.67 0.308 2.67 0.409 6.00 1.5910 4.33 0.60(a) Set up the relevant null and alternative hypothesis.(b) Write down the test statistic to be used for testing the hypothesis.(c) What is the sampling distribution of the test statistic if the null hypothesis is true?(d) If the level of signicance = 1%, what is the critical value? You can use Minitab for this.(e) Write down the rejection region.(f) Based on the data, do you reject the null hypothesis? Justify.4. The following data is a random sample from the montly performance of stock in Apple Computer since itsinception in 1980. Formulate a Simple Linear Regression Model with Apple return as the response and theMarket return (return on a value weighted portfolio that puchases stock in proportion to the size of companyrather than one of each stock) as the predictor.3Apple Return Market Return-0.0234657 0.00981617-0.0171103 -0.00445630.08870967 0.011710790.02542373 0.001401990.02641509 0.00746754-0.0608108 -0.0132820.00675676 0.010031530.03389831 0.001526370.01989026 0.002183380.05573722 0.0132828(a) Is there statistically signicant linear association between returns on stock in Apple and returns on theMarket? Justify by constructing and interpreting the ANOVA table.(b) Test the hypothesis that the intercept (0) of the regression model is zero. Write down the null andalternative hypothesis and compute the value of the test statistic and compare with the critical value.(c) Test the hypothesis that the slope (1) of the regression model is signicantly dierent from 1. Writedown the null and alternative hypothesis and compute the value of the test statistic and compare withthe critical value.4