# barcode font reporting services 0.476x0 (Problem 8.11), sy.x in Software Generate QR Code JIS X 0510 in Software 0.476x0 (Problem 8.11), sy.x

0.476x0 (Problem 8.11), sy.x
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1.28 (Problem 8.43).
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(a) If x0 65.0, we find [compare Problem 8.45(a)] the 95% confidence limits 66.76 1.07 inches, i.e., we can be about 95% confident that the mean height of all sons whose fathers heights are 65.0 inches will lie between 65.7 and 67.8 inches. (b) If x0 70.0, we find [compare Problem 8.45(b)] the 95% confidence limits 69.14 1.45 inches, i.e., we can be about 95% confident that the mean height of all sons whose fathers heights are 70.0 inches will lie between 67.7 and 70.6 inches.
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Sampling theory of correlation 8.47. A correlation coefficient based on a sample of size 18 was computed to be 0.32. Can we conclude at a significance level of (a) 0.05, (b) 0.01 that the corresponding population correlation coefficient is significantly greater than zero
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We wish to decide between the hypotheses (H0: r t r !n !1 2 r2 0) and (H1: r 0.32 !18 2 !1 (0.32)2 0). 1.35
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(a) On the basis of a one-tailed test of Student s distribution at a 0.05 level, we would reject H0 if t t0.95 1.75 for 18 2 16 degrees of freedom. Therefore, we cannot reject H0 at a 0.05 level. (b) Since we cannot reject H0 at a 0.05 level, we certainly cannot reject it at a 0.01 level.
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8.48. What is the minimum sample size necessary in order that we may conclude that a correlation coefficient of 0.32 is significantly greater than zero at a 0.05 level
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At a 0.05 level using a one-tailed test of Student s distribution, the minimum value of n must be such that 0.32 !n 2 !1 (0.32)2 For n For n For n 26, n 27, n 28, n 24, t0.95 25, t0.95 26, t0.95 28. t0.95 1.71, t 1.71, t 1.71, t for n 2 degrees of freedom (0.32)2 (0.32)2 (0.32)2 1.65. 1.69. 1.72.
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0.32 !24> !1 0.32 !25> !1 0.32 !26> !1
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Then the minimum sample size is n
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CHAPTER 8 Curve Fitting, Regression, and Correlation
8.49. A correlation coefficient based on a sample of size 24 was computed to be r 0.75. Can we reject the hypothesis that the population correlation coefficient is as small as (a) r 0.60, (b) r 0.50, at a 0.05 significance level
(a) Z 1.1513 log a 1 1 0.75 b 0.75 sZ The standardized variable is then z Z sZ mZ 0.9730 0.6932 0.2182 1.28 0.9730, 1 !n mZ 1.1513 log a 1 !21 0.2182 1 1 0.60 b 0.60 0.6932,
At a 0.05 level of significance using a one-tailed test of the normal distribution, we would reject the hypothesis only if z were greater than 1.64. Therefore, we cannot reject the hypothesis that the population correlation coefficient is as small as 0.60. (b) If r 0.50, mZ 1.1513 log 3 0.5493 and z (0.9730 0.5493)>0.2182 reject the hypothesis that the population correlation coefficient is as small as r significance. 1.94. Therefore, we can 0.50 at a 0.05 level of
8.50. The correlation coefficient between physics and mathematics final grades for a group of 21 students was computed to be 0.80. Find 95% confidence limits for this coefficient.
Since r 0.80 and n Z 21, 95% confidence limits for m2 are given by 1.1513 log a 1 1 r b r 1.96a 1 2n 3 b 1.0986 0.4620
1.96sZ
Then mZ has the 95% confidence interval 0.5366 to 1.5606. If If mZ mZ 1.1513 log a 1.1513 log a 1 1 1 1 r b r r b r 0.5366, 1.5606, r r 0.4904. 0.9155.
Therefore, the 95% confidence limits for r are 0.49 and 0.92.
8.51. Two correlation coefficients obtained from samples of size n1 28 and n2 35 were computed to be r1 0.50 and r2 0.30, respectively. Is there a significant difference between the two coefficients at a 0.05 level