Problem 10.47 HSV-2 is a STD. As part of the third National Health andNutrition
ID: 2954338 • Letter: P
Question
Problem 10.47 HSV-2 is a STD. As part of the third National Health andNutrition Examination Survey, prevalence of HSV-2 was determined infour regions of the US. The data are given in the followingtable.HSV-2 Region Sample size Number Percent Northeast 1488 323 21.7 Midwest 2070 381 18.4 South 5323 1,320 24.8 West 2698 712 26.4
a) Use a chi-square test to compare the prevalence rates atalpha = .01. (The value of the chi-square statistic isX2s = 49.77) b) Verify the value of X2s given inpart (a) HSV-2 is a STD. As part of the third National Health andNutrition Examination Survey, prevalence of HSV-2 was determined infour regions of the US. The data are given in the followingtable.
HSV-2 Region Sample size Number Percent Northeast 1488 323 21.7 Midwest 2070 381 18.4 South 5323 1,320 24.8 West 2698 712 26.4
a) Use a chi-square test to compare the prevalence rates atalpha = .01. (The value of the chi-square statistic isX2s = 49.77) b) Verify the value of X2s given inpart (a)
Explanation / Answer
(a) Here we have 3 degrees of freedom (#Regions - 1), so thecritical value of Chi-Square is 11.35 for alpha = 0.01 Clearly X2s = 49.77 exceedsX2crit = 11.35, thus the prevalance rates arenot equal for all four regions of the US. (b) To compute X2s for this problem, wecan start out with the observed frequency table: Observed NE MW S W STD 323 381 1320 712 2736 NO STD 1165 1689 4003 1986 8843 1488 2070 5323 2698 11579 The row/column sums are in bold, the grand total in red. Next, the expected frequencies for each cell is equal toRowSum*ColumnSum/GrandTotal For example, the expected number of people with STD in theNortheast is 2736*1488/11579, and with NO STD 8843*1488/11579, andso on. Expect NE MW S W STD 351.5992745 489.1199585 1257.770792 637.509975 NO STD 1136.400725 1580.880041 4065.229208 2060.490025 Chi^2 = (O-E)^2/E = (323 - 351.6)^2/351.6 + (1165 -1136.4)^2/1136.4 + (381 - 489.1)^2/489.1 + ... + (1986 -2060.5)^2/2060.5 = 49.77
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