Question

4. Here's a simple question that makes a big mess: "Are you more hard-working than the average (median) UCSD student?" You might wonder what percentage, p, of UCSD students would say "yes" to this (if you force a yes/no binary a. Set up hypotheses that make sense for this scenario. Use a two-sided alternative and give a reason why p might be larger than the value set in the null hypothesis, and a reason why p might be less. b. You conduct a study and ask some random Math 183 students the question. Your data give a 92% CI of [28.170%, 43.4966%). Explain what inference condition has been violated. Then, find the sample size used and the number of students that said yes in our sample

Answer 1

a)

Null hypothesis: There is no difference in proportion;

P=0.5

Alternate hypothesis: There is a significant difference in proportion;

p 0.5 (two sided alternative)

b)

There are three basic conditions for inference on proportion,

1) Random => satisfied as data values are randomly selected

2) Normal => Satisfied

3) Independent => Not satisfied as the data values are from same MATH students. hence there responses will be biased.

proportion of students say 'yes' is the middle value of 92% CI,

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