Question

Examining Genetic Alleles in Fast-Twitch Muscles

A study 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. (Open-ended, typed answer)

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. (Open-ended, typed answer)

c) Compare the p-values and conclusions of the two methods. (Open-ended, typed answer)

Answer 1

Answer:-

Given That:-

A study 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. (Open-ended, typed answer)?

Testing whether the proportions are equal or not

Expected values are

for both observed values are 244 & 192

Test Statistic

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. (Open-ended, typed answer)?

Degree of freedom = n-1 = 2-1 = 1

Using chi-square  distribution table with test statistic (6202) &dof(1), this gives as p - value=0.0125

Here ,p- value (0.128)<significance level (0.05).

So, we will adjucent the null hypothesis

c) Compare the p-values and conclusions of the two methods.?

There are sufficient evidence to conclude that the two options are not equally likely.

If null hypothesis true

we can conclude that the two options are equally likely.