Exercise 7.23 discusses a study investigating the ACTN3 genotypes RR, RX, and XX. The same study also examines the ACTN3 genetic alleles R and X, also associated with fast-twitch muscles. Of the 436 people in this sample, 244 were classified R and 192 were classified X. Does the sample provide evidence that the two options are not equally likely?
(a) Conduct the test using a chi-square goodness-of- fit test. Include all details of the test.
(b) Conduct the test using a test for a proportion, using H₀: p = 0.5 where p represents the proportion of the population classified R. Include all details of the test.
(c) Compare the p-values and conclusions of the two methods.

Exercise 7.23

Chisquare tests are common in genetics. A gene called ACTN3 encodes a protein which functions in fasttwitch muscles. People have different variants of this gene, classified as RR, RX, or XX. Computer output is shown for testing whether the proportions in these categories are 0.25, 0.50, and 0.25, respectively. The observed counts come from a study conducted in Australia.

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Chi-Square Goodness-of-Fit Test for Observed Counts Test Proportion 0.25 Contribution to Chi-Sq 4.04587 0.29358 7.71560 Observed Expected Category 109 RR 130 226 RX 0.50 0.25 218 109 80 XX Chi-Sq P-Value 0.002 2 12.0550 DF 436