You are testing the claim that having lights on at night increases weight gain (abstract). A sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. Test the claim using a 2% level of significance. Assume the population variances are unequal and that the weight changes are normally distributed. Give answers to 3 decimal places.

Data available at StatKey, choose Mice Wgt Gain-2e data set

Light ($\displaystyle {x}_{{1}}$)	Dark ($\displaystyle {x}_{{2}}$)
1.71	2.27
4.67	2.53
4.99	2.83
5.33	4
5.43	4.21
6.94	4.6
7.15	5.95
9.17	6.52
10.26
11.67

What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem.

H₀: Select an answer x̅₂ σ² x̅₁ s² μ₂ p μ₁  ? = ≥ ≠ ≤ > <  Select an answer σ² s² μ₂ p x̅₁ x̅₂ 0 μ₁

H_a: Select an answer x̅₁ p μ₁ μ₂ s² σ² x̅₂  ? = ≤ ≠ < ≥ >  Select an answer μ₁ 0 μ₂ σ² s² x̅₁ p x̅₂

Based on the hypotheses, find the following:

Test Statistic = (Hint: difference in means from H_a)

p-value =

The correct decision is to Select an answer reject the claim accept the null hypothesis reject the null hypothesis accept the alternative hypothesis fail to reject the null hypothesis .

The correct summary would be: Select an answer There is not enough evidence to reject the claim There is enough evidence to support the claim There is enough evidence to reject the claim There is not enough evidence to support the claim that sleeping with lights on can cause weight gain.

Fonken, L., et. al., "Light at night increases body mass by shifting time of food intake," Proceedings of the National Academy of Sciences, October 26, 2010; 107(43): 18664-18669. abstract