1051 Let p 1 and p 2 denote the probability of survival for the treated group

1051 let p 1 and p 2 denote the probability of

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10.51 Let p 1 and p 2 denote the probability of survival for the treated group (with carbolic acid) and the control group (without carbolic acid), respectively. We formulate the hypotheses: versus . The test statistic is . Since H 1 is two-sided and , the rejection region is (illustrated below). ffddb18f5169bd51dc4679f2ce66163f8ea7b21b 13
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We calculate the following: Pooled estimate , Observed z is , which lies in R . Hence, H 0 is rejected at . Furthermore, the associated p - value. This means that H 0 would be rejected with as small as 0.0036. As such, a difference in the survival rates is strongly demonstrated by the data. 10.52 Estimated S.E. = So, a 95% confidence interval for is given by () or (0.11, 0.51). 10.55 (a) Let p 1 and p 2 denote the probability of having prominent wrinkles for smokers and non-smokers, respectively. We formulate the hypotheses: versus . The test statistic is . Since H 1 is right-sided, the rejection region is of the form . We calculate the following: ffddb18f5169bd51dc4679f2ce66163f8ea7b21b 14
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Pooled estimate , Observed z is The associated p -value is is less than 0.0002. So, there is very strong evidence in support of H 1 . (b) A direct causal relation between smoking and wrinkled skin cannot be readily concluded. Various psycho-physiological factors could influence both the smoking habit and the presence of wrinkled skin. 10.58 (a) We formulate the hypotheses: versus . The test statistic is , where we identify as , respectively. Since H 1 is right-sided and , the rejection region is . We calculate the following: Pooled estimate , Observed z is , which does not lie in R . Hence, H 0 is not rejected at . (b) We formulate the hypotheses: versus . The test statistic is , where we identify as , respectively. Since H 1 is right-sided, the rejection region is of the form . We calculate the following: ffddb18f5169bd51dc4679f2ce66163f8ea7b21b 15
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Pooled estimate , Observed z is The associated p -value is less than 0.0002. Hence, the data strongly substantiate H 1 . Answer Keys Chapter 11 11.1 The points on the line for and are (1,5) and (4,14) respectively. The intercept is 2 and the slope is 3. ffddb18f5169bd51dc4679f2ce66163f8ea7b21b 16
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11.2 (a) If , then . (b) We must determine the smallest x value such that . Solving this inequality yields . So, we must sell at least 16 batteries in a month in order to make a profit. 11.3 (a) Predictor variable x = duration of training Response variable y = performance in skilled job (b) Predictor variable x = average number of cigarettes smoked daily Response variable y = CO level in blood (c) Predictor variable x = Humidity level in environment Response variable y = Growth rate of fungus (d) Predictor variable x = Expenditures in promoting product Response variable y = Amount of product sales 11.10 (a) At , . At 6 x =, . (b) No, only the mean is larger. By chance the error e at , which has standard deviation 3, could be quite negative and/or the error at very large. 11.11 (a) At , . At 5 x =, .
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