HW2-answer

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Feb 20, 2024

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2.6.7 Dopamine is a chemical that plays a role in the trans- mission of signals in the brain. A pharmacologist measured the amount of dopamine in the brain of each of seven rats. The dopamine levels (nmoles/g) were as follows:*! 6.8 53 6.059 68 74 6.2 (a) Calculate the mean and SD. (b) Determine the median and the interquartile range. (c) Replace the observation 74 by 10.4 and repeat parts (a) and (b). Which of the descriptive measures display robustness and which do not? Answer (2.5pt): 2.6.7 (a) ¥ =6.343; s =0.7020. (b) Median =6.2; Q,=5.9,Q, =6.8,IQR=6.8-5.9=9. (¢c) New y=6.77; new s = 1.68; new median = 6.2, new IQR = 0.9. The median and interquartile range display resistance in that they do not change. The standard deviation changes greatly, showing its lack of resistance. The mean changes a modest amount. 2.6.11 Listed in increasing order are the serum creatine phosphokinase (CK) levels (U/l) of 36 healthy men (these are the data of Example 2.2.6): 25 62 8 95 110 139 42 64 8 95 113 145 48 67 84 100 118 151 57 68 92 101 119 163 58 70 93 104 121 201 60 78 94 110 123 203 The sample mean CK level is 98.3 U/l and the SD is 40.4 U/l. What percentage of the observations are within (a) 1 SD of the mean? (b) 2 SDs of the mean? (c) 3 SDs of the mean? Answer (2.5pt): 2.6.11 (a) y=+sis 57.9 to 138.7; this interval contains 26/36 or 72% of the observations. (b) y+2sis 17.5 to 179.1; this interval contains 34/36 or 94% of the observations. (¢) y+3sis-22.9 to 219.5; this interval contains 36/36 or 100% of the observations.
2.6.12 Compare the results of Exercise 2.6.11 with the predictions of the empirical rule. Answer (2.5pt): 2.6.12 According to the Empirical Rule, we expect 68% of the data to be within one SD of the mean; this is close to the observed 72%. We expect 95% of the data to be within two SDs of the mean; this is quite close to the observed 94%. We expect over 99% of the data to be within three SDs of the mean; in fact, 100% of the observations are in this interval. 2.7.2 The mean and SD of a set of 47 body temperature measurements were as follows:* y = 36497°C s =0.172°C If the 47 measurements were converted to °F, (a) What would be the new mean and SD? (b) What would be the new coefficient of variation? Answer (2.5pt): 2.7.2 (a) Mean = (36.497)(1.8) + 32 = 97.695; SD = (0.172)(1.8) = 0.310 (b) Coefficient of variation = .310/97.695 = 0.003 or 0.3%. [Remark: This is not the same as the original coefficient of variation, which 1s 0.172/36.497 = 0.005 or 0.5%.]
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