Question

Feminized faces in TV commercials. Television commercials most often employ females or “feminized” males to pitch a company’s product. Research published in Nature (August 27 1998) revealed that people are, in fact, more attracted to “feminized” faces, regardless of gender. In one experiment, 50 human subjects viewed both a Japanese female face and a Caucasian male face on a computer. Using special computer graphics, each subject could morph the faces (by making them more feminine or more masculine) until they attained the “most attractive” face. The level of feminization x (measured as a percentage) was measured.

a. For the Japanese female face, x = 10.2% and s = 31.3%. The researchers used this sample information to test the null hypothesis of a mean level of feminization equal to 0%. Verify that the test statistic is equal to 2.3.

b. Refer to part a. The researchers reported the p-value of the test as p = .021. Verify and interpret this result.

(I dont understand part b)

Answer 1

Since you have mentioned that you have an issue in part b of the question, here is an explanation for the same-

Firstly, P-value is a probability value at which you just reject the null hypothesis.

On testing the null hypothesis in part a, it was found that t-statistic is 2.3

Hence we are asked to find the probability value that will allow us to reject the null hypothesis.

From the t- table, we check a value close to 2.3 corresponding to (n-1) degrees of freedom i.e. 49.

But we would not find 49 degrees of freedom on the table, but 40 and the next value will be 60 degrees of freedom.

So we would find t₅₀ by finding the mid value of 40 and 60, and would get its corresponding value simultaneously, which came out to be 2.3 (approximately).

Now we would check for the corresponding probability in the table, which was 0.02 for a two tailed test.

Hence the p-value at which we could reject the null hypothesis is 0.02 (as given in the question).

Interpretation : If we reject the null hypothesis that the level of feminization is 0%, then one would find a difference or more in about 2% of studies due to the error in sampling.

HOPE THIS HELPS!