In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. In the following data pairs, A represents the cost of living index for utilities and B represents the cost of living index for transportation. The data are paired by metropolitan areas in the United States. A random sample of 46 metropolitan areas gave the following information. A: 90 82 84 107 85 102 89 123 104 B: 100 92 104 101 111 108 93 115 113 A: 118 133 104 84 80 77 90 92 90 B: 106 95 110 112 105 93 119 99 109 A: 106 95 110 112 105 93 119 99 109 B: 96 109 103 107 103 102 101 86 94 A: 109 113 90 121 120 85 91 91 97 B: 88 100 104 119 116 104 121 108 86 A: 95 115 99 86 88 106 80 108 90 87 B: 100 83 88 103 94 125 115 100 96 127 Do the data indicate that the U.S. population mean cost of living index for utilities is less than that for transportation in these areas? Use ? = 0.05. (Let d = A − B.) (a) What is the level of significance? .05 (b) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: ?d = 0; H1: ?d < 0; left-tailed (c) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately normal distribution. (d) What is the value of the sample test statistic? (Round your answer to three decimal places.) ????????? (e) Find (or estimate) the P-value. P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005 (f) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? (A)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (B)At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (C)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (D) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. In the following data pairs, A represents the cost of living index for utilities and B represents the cost of living index for transportation. The data are paired by metropolitan areas in the United States. A random sample of 46 metropolitan areas gave the following information. A: 90 82 84 107 85 102 89 123 104 B: 100 92 104 101 111 108 93 115 113 A: 118 133 104 84 80 77 90 92 90 B: 106 95 110 112 105 93 119 99 109 A: 106 95 110 112 105 93 119 99 109 B: 96 109 103 107 103 102 101 86 94 A: 109 113 90 121 120 85 91 91 97 B: 88 100 104 119 116 104 121 108 86 A: 95 115 99 86 88 106 80 108 90 87 B: 100 83 88 103 94 125 115 100 96 127 Do the data indicate that the U.S. population mean cost of living index for utilities is less than that for transportation in these areas? Use ? = 0.05. (Let d = A − B.) (a) What is the level of significance? .05 (b) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: ?d = 0; H1: ?d < 0; left-tailed (c) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately normal distribution. (d) What is the value of the sample test statistic? (Round your answer to three decimal places.) ????????? (e) Find (or estimate) the P-value. P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005 (f) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? (A)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (B)At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (C)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (D) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

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Description: In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-val

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

In the following data pairs, A represents the cost of living index for utilities and B represents the cost of living index for transportation. The data are paired by metropolitan areas in the United States. A random sample of 46 metropolitan areas gave the following information.

A:	90	82	84	107	85	102	89	123	104
B:	100	92	104	101	111	108	93	115	113

A:	118	133	104	84	80	77	90	92	90
B:	106	95	110	112	105	93	119	99	109

A:	106	95	110	112	105	93	119	99	109
B:	96	109	103	107	103	102	101	86	94

A:	109	113	90	121	120	85	91	91	97
B:	88	100	104	119	116	104	121	108	86

A:	95	115	99	86	88	106	80	108	90	87
B:	100	83	88	103	94	125	115	100	96	127

Do the data indicate that the U.S. population mean cost of living index for utilities is less than that for transportation in these areas? Use ? = 0.05. (Let d = A − B.)

(a) What is the level of significance? .05

(b) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H₀: ?_d = 0; H₁: ?_d < 0; left-tailed

(c) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately normal distribution.

(d) What is the value of the sample test statistic? (Round your answer to three decimal places.) ?????????

(e) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

(f) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

(A)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(B)At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(C)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

(D) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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