Question

The UF athletic department wanted to determine if students came to more than 4 home football games on average per season. They randomly surveyed 10 students. Assume all responses were independent of each other. Can we assume normal distribution of the sampling distribution of the sample mean?

A. No, not enough students were sampled
B. No, the randomization condition was not met
C. No the independence assumption was not met
D.Yes

Answer 1

Answer: Option D if we consider the survey as one with only one variable, where the options are "yes, i asisted to more than 4 games" or no.

Explanation:

We know that they randomly surveyed 10 students. so the randomization condition was meet, and we know that the students responses were independnt of each other, so options B and C can be discarded.

Now, only 10 students where surveyed, the confidence interval will not be narrow at all.

For example, acccording to StaisticsSolutions, in regression analysis the minimum is actually 10 subjects er variable.

If the researchers are asking the number of games asisted per student, the number of variables will be big, while if the question is "you attended to more than 4 or not?" there is only one variable, then in this case 10 students will be enough.