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Source: Bureau of Labor Statistics.
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CHAPTER 8 Curve Fitting, Regression, and Correlation
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8.105. Refer to Table 8-43. (a) Graph the data. (b) Find a least-squares line fitting the data and construct its graph. (c) Compute the trend values and compare with the actual values. (d) Predict the price index for medical care during 1958 and compare with the true value (144.4). (e) In what year can we expect the index of medical costs to be double that of 1947 through 1949, assuming present trends continue
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Table 8-43
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Year Consumer Price Index for Medical Care (1947 1949 100) 1950 106.0 1951 111.1 1952 117.2 1953 121.3 1954 125.2 1955 128.0 1956 132.6 1957 138.0
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Source: Bureau of Labor Statistics. 8.106. Refer to Table 8-44. (a) Graph the data. (b) Find a least-squares parabola fitting the data. (c) Compute the trend values and compare with the actual values. (d) Explain why the equation obtained in (b) is not useful for extrapolation purposes. Table 8-44 Year Birth Rate per 1000 Population 1915 25.0 1920 23.7 1925 21.3 1930 18.9 1935 16.9 1940 17.9 1945 19.5 1950 23.6 1955 24.6
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Source: Department of Health and Human Services.
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8.64. (a) y 1 3 5 x or 7 y 0.333 0.714x (b) x 1 9 y or x 7 1.00 1.29y
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8.65. (a) 3.24, 8.24 (b) 10.00 8.67. (b) y 8.68. y 4.000
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8.66. (b) y 2.408
29.13 0.612y 2.51
0.661x (c) x
1.15y (d) 79 (e) 95
0.500x (c) x 3) 0.733(x
3.20(x
3)2 or y
1.20x
0.733x2
8.69. (b) d 8.70. (b) y 8.71. (a) z
1.096v
0.08786v2
(c) 170 ft, 516 feet 32.14e0.3556x (d) 387
32.14(1.427)x or y 61.40 3.65x
32.14(10)0.1544x or y (b) 40
2.54y
8.72. (a) 1.304
(b) 1.443
8.73. (a) 24.50 (b) 17.00 (c) 7.50 8.76. (a) 0.8961 (b) y 8.77. (a) 0.958 (b) 0.872 80.78
8.74. 0.5533
8.75. 1.5
1.138x (c) 132 0.8x 12 (b) x 0.45y 1
8.78. (a) y
CHAPTER 8 Curve Fitting, Regression, and Correlation
8.79. (a) 1.60 (b) 1.20 8.83. 3.12 8.87. 1.0000 8.84. 0.9927
8.81. 75%
8.82. (a)
8.85. rrank
8.86. (a) 0.5182 (b) 0.9318 0.28
8.88. (a) 2.00
0.21 (b) 2.00
8.89. (a) Using a one-tailed test, we can reject the hypothesis. (b) Using a one-tailed test, we cannot reject the hypothesis. 8.90. (a) 37.0 8.92. (a) 1.138 3.6 (b) 37.0 4.9 8.91. (a) 37.0 19.2 (c) 132.0 1.5 (b) 37.0 5.4 2.1
0.398 (b) 132.0
8.93. (a) Yes. (b) No. 8.95. (a) 0.2923 and 0.7951 8.96. (a) 0.3912 and 0.7500 8.97. 0.7096 and 0.9653 8.100. 0.5440
8.94. (a) No. (b) Yes. (b) 0.1763 and 0.8361 (b) 0.3146 and 0.7861 8.98. (a) yes (b) no 4.44x 142.22 8.99. 0.8 (b) 141.9 and 177.5 pounds 8.104. 0.9263 107.1 4.38x if x-unit is 1 year
8.101. (a) y
8.102. (a) 16.92 1b (b) 2.07 in
8.103. 0.4961 and 0.7235
8.105. (b) y 122.42 2.19x if x-unit is 2 year and origin is at Jan. 1, 1954; or y and origin is at July 1, 1950 (d) 142.1 (e) 1971 8.106. (b) y 18.16 0.1083x origin at July 1, 1935
0.4653x2, where y is the birth rate per 1000 population and x-unit is 5 years with
CHAPTER 12 CHAPTER 9
Analysis of Variance
The Purpose of Analysis of Variance
In 7 we used sampling theory to test the significance of differences between two sampling means. We assumed that the two populations from which the samples were drawn had the same variance. In many situations there is a need to test the significance of differences among three or more sampling means, or equivalently to test the null hypothesis that the sample means are all equal.
EXAMPLE 9.1 Suppose that in an agricultural experiment, four different chemical treatments of soil produced mean wheat yields of 28, 22, 18, and 24 bushels per acre, respectively. Is there a significant difference in these means, or is the observed spread simply due to chance
Problems such as these can be solved by using an important technique known as the analysis of variance, developed by Fisher. It makes use of the F distribution already considered in previous chapters.
One-Way Classification or One-Factor Experiments
In a one-factor experiment measurements or observations are obtained for a independent groups of samples, where the number of measurements in each group is b. We speak of a treatments, each of which has b repetitions or replications. In Example 9.1, a 4. The results of a one-factor experiment can be presented in a table having a rows and b columns (Table 9-1). Here xjk denotes the measurement in the jth row and kth column, where j 1, 2, . . . , a and k 1, 2, . . . , b. For example, x35 refers to the fifth measurement for the third treatment. Table 9-1 Treatment 1 Treatment 2 ( Treatment a xa1 x11 x21 x12 x22 ( xa2 c xab xa. # c x 1b c x 2b x1. # x2. #
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