Question

Researchers wished to compare two populations of infants with respect to mean age at which they walked alone. The following data (ages in months) were collected. Sample from Population A: 9.5, 10.5, 9.0, 9.75, 10.0, 13.0, 10.3 Sample from Population B: 12.5, 9.5, 13.5, 13.75, 12.0, 13.75 Suppose that the populations do not follow a normal distribution. Which of the following is true?

(A) The two-sample t-test cannot be used. (B) For a given significance level, the probability of a Type II error is lower for the two-sample t-test than for the corresponding nonparametric test.   (C) For a given significance level, the probability of a Type II error is higher for the two-sample t-test than for the corresponding nonparametric test.   (D) A nonparametric test cannot be used. (E) For a given significance level, the probability of a Type I error is lower for the two-sample t-test then for the corresponding nonparametric test.   (F) For a given significance level, the probability of a Type I error is higher for the two-sample t-test than for the corresponding nonparametric test.

Answer 1

Correct options are:

(A) The two-sample t-test cannot be used. (since population are not normal and sample size<30)

B) For a given significance level, the probability of a Type II error is lower
for the two-sample t-test than for the corresponding nonparametric test.  

(please choose A only if only 1 option is supposed to be chosen)