A cross between white and yellow summer squash gave progeny of the following counts:
| Color | White | Yellow | Green |
| ----------------- | ----- | ------ | ----- |
| Number of progeny | 155 | 40 | 10 |
A researcher wants to test if these data are consistent with the 12:3:1 ratio predicted by a certain genetic model. Which one is the correct R code to carry out the chi-square test?
A. `x <- c(155,40,10)`
`chisq.test(x, p=c(12 / 16, 3 / 16, 1 / 16))`
B. `x <- c(155,40,10)`
`chisq.test(x,p=c(12,3,1))`
C. `x <- c(153.75,38.4375,12.8125)`
`chisq.test(x,p=c(12/16,3/16,1/16))`
D. `x <- c(155,40,10)`
`chisq.test(x, p=c(0.75,0.28,0.6))`
Answer (1)
Observed frequencies: 155, 40, 10.
Expected ratio: 12:3:1, which translates to probabilities 12/16, 3/16, 1/16.
The correct R code uses chisq.test(x, p=c(12/16, 3/16, 1/16)) , where x contains the observed frequencies and p contains the expected probabilities.
The correct R code is therefore: chisq.test(x, p=c(12/16, 3/16, 1/16)) where x <- c(155, 40, 10) .
Explanation
Analyze the problem and data We are given observed data for the colors of progeny from a cross between white and yellow summer squash: White (155), Yellow (40), and Green (10). We want to determine the correct R code to perform a chi-square test to see if these data are consistent with a 12:3:1 ratio.
Calculate expected probabilities The chi-square test requires observed frequencies and expected probabilities. The observed frequencies are 155, 40, and 10. The expected ratio is 12:3:1. To convert the ratio to probabilities, we divide each number in the ratio by the sum of the ratio numbers: 12 + 3 + 1 = 16. Thus, the expected probabilities are 12/16, 3/16, and 1/16.
Construct the correct R code The correct R code should use the chisq.test() function with the observed frequencies and expected probabilities. The observed frequencies should be a vector x <- c(155, 40, 10) , and the expected probabilities should be a vector p = c(12/16, 3/16, 1/16) . Therefore, the correct R code is chisq.test(x, p=c(12/16, 3/16, 1/16)) .
State the final answer The correct R code is:
x <- c(155,40,10)
chisq.test(x, p=c(12/16, 3/16, 1/16))
Examples
A geneticist studies the inheritance of traits in plants. They observe the offspring of a cross and want to determine if the observed ratios of different traits match the expected ratios predicted by Mendelian genetics. The chi-square test helps them assess the goodness of fit between the observed and expected values, providing evidence to support or reject their genetic model. For example, if the geneticist expects a 3:1 ratio of dominant to recessive traits, they can use the chi-square test to see if their observed data significantly deviates from this ratio. The R code chisq.test(x, p=c(0.75, 0.25)) can be used, where x is a vector of observed counts and p is a vector of expected probabilities (3/4 and 1/4).
