Question

A survey of MATH&146 students during the Fall 2014 quarter asked students whether they ate breakfast the morning of the survey. Results are as follows:

	Female	Male	Total
Yes	40	14	52
No	12	11	23
Total	50	25	75

a) To determine if there was a difference in the proportions of females and males eating breakfast, what claims should be tested?

H₀: pF−pM=pF-pM=
H_A: pF−pM≠pF-pM≠

b) What is the difference in the proportions of females and males that ate breakfast before the survey?

c) Below is a dot plot of 60 simulation results computed under the null hypothesis. In each simulation, the summary value reported was the difference in the proportions eating breakfast between females and males. Estimate the p-value and write a conclusion for the hypothesis test in plain language.

p-value =

Conclusion (Don't just say reject or fail to reject. Explain what the p-value means in the context of this problem.

Answer 1

(a) The hypothesis being tested is:

H0: p1 = p2

Ha: p1 ≠ p2

(b) The difference in the proportions of females and males that ate breakfast before the survey = 0.24

(c) p-value = 0.0291

Conclusion:

Since the p-value (0.0291) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there was a difference in the proportions of females and males eating breakfast.

p1	p2	pc
0.8	0.56	0.72	p (as decimal)
40/50	14/25	54/75	p (as fraction)
40.	14.	54.	X
50	25	75	n
	0.24	difference
	0.	hypothesized difference
	0.11	std. error
	2.18	z
	.0291	p-value (two-tailed)