Problem#04 A study of a pain relief medication was done using a treatment group and a placebo group. The results are shown in the table below, where the pain increase was recorded based on a scale from 0 to 5. The two samples are independent simple random samples. Use a 0.01 significance level to test the effectiveness of the medication. Treatment Placebo H1 H2 n 35 33 X 2.31 2.69 S 0.58 0.99Problem#05 An investigator analyzed the leading digits from checks issued by seven suspect companies. The frequencies were found to be 212, 144, 104, 54, 64, 48, 40, 43, and 57, and those digits correspond to the leading digits of: l, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.01 signicance level to test for goodness-offlt with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit 1 2 3 4 5 6 7 8 9 Actual Frequency 212 144 104 54 64 48 40 43 57 Benford's Law: Distribution of 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% Leading Digits Problem#06 For a simple random sample of pulse rates of women (measured in beats per minute), 11 = 146 and S = 13.3. The range of pulse rates of adults is known to have a normal distribution with a typical standard deviation of 10 beats per minute. Use the sample results with a 0.05 signicance level to test the claim that there is no difference between the women's pulse rates standard deviation and that of all adult population. Problem#07 The data show the time intervals after an eruption (to the next eruption) of a certain geyser. Find the regression equation, letting the rst variable be the independent (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of feet. Height(ft) 115 133 137 140 99 112 108 126 Interval after (min) 75 85 94 85 66 88 68 82 Problem#08 The blood pressure measurements of a single patient were taken by twelve different medical students and the results are listed below. systolic (x) 137 130 140 121 126 124 127 132 125 145 140 diastolic (y) 138 94 93 99 81 87 83 82 85 80 98 104 97 a) Select the corresponding scatterplot: O A. O B. O C. OD. 160 Ty 160 Ty 160 Ty 160 Ty O 120- O 120- o 120- Jo O 120- O 80- OO 80- O 8 o 80- 80- O O O o 40- O O O 40- O 40- O O O O 40- o O- X 8 X 8 X O X 40 80 120 160 0 40 80 120 160 of o 40 80 120 160 40 80 120 160 b) Find the value of the linear correlation coefficient r. c) At a = 0.05, is there sufficient evidence to conclude that there is a linear correlation between systolic and diastolic measurements?Problem#02 Listed in the accompanying table are heights (in.) of mothers and their first daughters. The samples are simple random samples and the women population heights have a distribution that is approximately normal. Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and their first daughters. Mother 62.0 64.5 65.0 63.7 65.5 62.0 67.0 63.5 66.0 67. Daughter 67.5 67.0 65.0 63.7 64.0 66.0 67.0 67.5 66.5 66