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Sex ratios (a) In a contingency table with r rows and 2 columns the observations in row i are n₁, and n;2, with row totals n₁. = n₁1 + n₁2, i = 1,2,...,r; the column totals are n.₁ and n2, with n.₁+n₂ = n, the total number of observations. Show that the x2 statistic for testing independence of the variables defining the rows and columns of the table can be written as X² n² n.1n.2i=1 - Σ (n₁₁ - n₁ n.₁/n) ² (nix n₁. Hence, or otherwise, show that it can be expressed as *-2 (2-4) (b) Samples of a certain species of insect were collected from two different locations, and the number of females was observed. There were 44 females in the 100 insects collected at the first location, and 86 females out of 200 insects at the second location. Test whether the proportions of females differ between the two locations. (c) A further sample of 200 insects is taken at a third location and found to contain 110 females. Consider the data from all three locations simultaneously, and test whether there are differences in the proportions of females between the three locations.

Sex ratios (a) In a contingency table with r rows and 2 columns the observations in row i are n₁, and n;2, with row totals n₁. = n₁1 + n₁2, i = 1,2,...,r; the column totals are n.₁ and n2, with n.₁+n₂ = n, the total number of observations. Show that the x2 statistic for testing independence of the variables defining the rows and columns of the table can be written as X² n² n.1n.2i=1 - Σ (n₁₁ - n₁ n.₁/n) ² (nix n₁. Hence, or otherwise, show that it can be expressed as *-2 (2-4) (b) Samples of a certain species of insect were collected from two different locations, and the number of females was observed. There were 44 females in the 100 insects collected at the first location, and 86 females out of 200 insects at the second location. Test whether the proportions of females differ between the two locations. (c) A further sample of 200 insects is taken at a third location and found to contain 110 females. Consider the data from all three locations simultaneously, and test whether there are differences in the proportions of females between the three locations.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
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Sex ratios (a) In a contingency table with r rows and 2 columns the observations in row i are n₁, and n;2, with row totals n₁ = n₁₁ +n₁2, i = 1,2,...,r; the column totals are n.₁ and n2, with n.₁+n₂ = n, the total number of observations. Show that the x2 statistic for testing independence of the variables defining the rows and columns of the table can be written as X² n² n.1n.2i=1 - Σ (n¡1 - n;.n.1/n)² n₁. Hence, or otherwise, show that it can be expressed as *-2 (2-4) (b) Samples of a certain species of insect were collected from two different locations, and the number of females was observed. There were 44 females in the 100 insects collected at the first location, and 86 females out of 200 insects at the second location. Test whether the proportions of females differ between the two locations. (c) A further sample of 200 insects is taken at a third location and found to contain 110 females. Consider the data from all three locations simultaneously, and test whether there are differences in the proportions of females between the three locations.
Transcribed Image Text:Sex ratios (a) In a contingency table with r rows and 2 columns the observations in row i are n₁, and n;2, with row totals n₁ = n₁₁ +n₁2, i = 1,2,...,r; the column totals are n.₁ and n2, with n.₁+n₂ = n, the total number of observations. Show that the x2 statistic for testing independence of the variables defining the rows and columns of the table can be written as X² n² n.1n.2i=1 - Σ (n¡1 - n;.n.1/n)² n₁. Hence, or otherwise, show that it can be expressed as *-2 (2-4) (b) Samples of a certain species of insect were collected from two different locations, and the number of females was observed. There were 44 females in the 100 insects collected at the first location, and 86 females out of 200 insects at the second location. Test whether the proportions of females differ between the two locations. (c) A further sample of 200 insects is taken at a third location and found to contain 110 females. Consider the data from all three locations simultaneously, and test whether there are differences in the proportions of females between the three locations.
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