Statistics Homework Solutions 134

Statistics Homework Solutions 134 - 134 CHAPTER 6 0 44....

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Unformatted text preview: 134 CHAPTER 6 0 44. Since the alternate hypothesis is of the form µ ¨ ¡¥ ¡ ¤£ 40. µ0 , the P-value is the area ¤ ¥ £ ¨ ¨ ¡ ¨ ¡ ¤ ¡ ¡ ¡ 0 3300. ¨ ¡ Thus P 7 58 0 44. 40 versus H1 : µ ¡ ¡ 39 6 40 z to the left of z 58. The null and alternate hypotheses are H0 : µ ¡ 7, n § 39 6, s ¡ 9. (a) X (b) If the mean air velocity were 40 cm/s, the probability of observing a sample mean as small as the value of 39.6 that was actually observed would be 0.33. Since 0.33 is not a small probability, it is plausible that the mean air velocity is 40 cm/s or more. 11. (ii) 5. The null distribution specifies that the population mean, which is also the mean of X , is the value on the boundary between the null and alternate hypotheses. 13. X ¡ 0 1. The null and alternate hypotheses are H0 : µ 5 0 versus H1 : µ ¨ ¨ ¡ n 5 0. ¡ ¤£ σ ¨ ¡ 5 2 and σX ¨ ¡ ¨ ¡ 0 0456. ¨ 0 2153. The null and alternate hypotheses are H0 : µ ¨ ¡ ¤£ ¨ ¤ 3 5 versus ¨ ¨ ¡ ¢ ¨ ¤£ ¡ ¨ 2 65. £ ©¥ ¨ ¡ ¨ ¤ ¡ 0 0040. µ0 , the P-value is the area to the right of z 2 65. ¨ ¡ Thus P ¡ ¨ (c) Since the alternate hypothesis is of the form µ ¡ ¡ 3 5 0 2153 ¨ ¡ ¡ ¨ 4 07114 ¨ ¡ z n ¨ ¤£ £ ©¥ ¨ (b) X 4 07114. From part (a), s H1 : µ 3 5. 0 2153. ¡ 87 ¨ ¡ ¨ ¡ 2 00819 ¨ ¡ ¨ n ¡ 15. (a) SE Mean = s 0 0228 µ 0 , the P-value is the sum of the ¨ ¡ 0 0228 Thus P ¡ z 5 2 5 0 0 1 2 00. Since the alternate hypothesis is of the form µ areas to the right of z 2 00 and to the left of z 2 00. Section 6.2 0 5. The larger the P-value, the more plausible the null hypothesis. 1. P 3. (iv). A P-value of 0.01 means that if H0 is true, then the observed value of the test statistic was in the most extreme 1% of its distribution. This is unlikely, but not impossible. ¨ ¡ ...
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