Chapter 11 Solutions - 245 Chapter 11 11.1(a = the mean score for all older students at this college(b If = 115 the sampling distribution of x in Normal

Chapter 11 Solutions - 245 Chapter 11 11.1(a = the mean...

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Chapter 11 11.1 (a) µ = the mean score for all older students at this college. (b) If 115 µ = , the sampling distribution of x in Normal with mean 115 and standard deviation 30 25 6 = or N(115, 6). See the sketch below (on the left). (c) Assuming is true, observing a mean of 118.6 or higher would not be surprising, but a mean of 125.7 or higher is less likely, and therefore provides more evidence against . (d) Yes, the sample size is not large enough ( 0 H 0 H 25 n = ) to use the central limit theorem for normality. (e) No, the older students at this college may not be representative of older students at other colleges in the USA. SSHA score Normal density curve 133 127 121 115 109 103 97 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 118.6 125.7 Hemoglobin level (g/dl) Normal density curve 12.6789 12.4546 12.2263 12.0000 11.7737 11.5474 11.3211 2.0 1.5 1.0 0.5 0.0 11.3 11.8 11.2 (a) µ = the mean hemoglobin level for all children of this age in Jordan. (b) If 12 µ = , the sampling distribution of x is Normal with mean 12 g/dl and standard deviation 1.6 50 0.2263 = g/dl. See the sketch above (on the right). (c) A result like 11.3 x = g/dl lies way down in the low tail of the density curve (over 3 standard deviations below the mean), while 11 . 8 g/dl is fairly close to the middle. If 12 µ = g/dl, observing a mean of 11.8 g/dl or smaller would not be too surprising, but a mean of 11.3 g/dl or smaller is extremely unlikely, and it therefore provides strong evidence that 12 µ < g/dl . (d) No, since the sample size is large ( n = 50), the central limit theorem says that the sampling distribution of x is approximately N(12 g/dl , 0 . 2263 g/dl). (e) No, we are told that this is sample, but we don’t know if these children were randomly selected from any larger population. The only way we can generalize to a larger population is if this sample is representative of the larger population. < ; . p . . 245
11.6 (a) 0 H and a H have been switched: The null hypothesis should be a statement of “no change.” (b) The null hypothesis should be a statement about µ , not x . (c) Our hypothesis should be “some claim about the population.” Whether or not it rains tomorrow is not such a statement. Put another way, hypothesis testing—at least as described in this text—does not deal with random outcomes, but rather with statements that are either true or false. Rain (or not) is a random outcome. 11.7 (a) Because the workers were chosen without replacement, randomly sampled from the assembly workers and then randomly assigned to each group, the requirements of SRS and independence are met. The question states that the differences in job satisfaction follow a Normal distribution. (b) Yes, because the sample size ( n = 18) is too small for the central limit theorem to apply.