The image contains two incomplete statements with dropdown menus for selecting answers:1. "The correct decision is to [Select an answer]." 2. "The correct summary would be: [Select an answer] that sleeping with lights on can cause weight gain."There are no graphs or diagrams in this image. ### Testing the Effect of Light on Weight Gain in MiceYou are testing the claim that having lights on at night increases weight gain. 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 6% 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](#)#### Data Table:| Light (x₁) | Dark (x₂) ||------------|-----------|| 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 | |#### Hypothesis Testing**What are the correct hypotheses? Select the correct symbols in the order they appear in the problem.**- **H₀ (Null Hypothesis):** ___ [Select an answer] ___ [Select an answer] ___- **Hₐ (Alternative Hypothesis):** ___ [Select an answer] ___ [Select an answer] ___**Based on the hypotheses, find the following:**- **Test Statistic =** ___ (Hint: difference in means from Hₐ)- **p-value =** ___Use this information to evaluate the hypothesis that constant light exposure affects weight gain compared to normal light/dark cycles.

Solution: First we find sample means and standard deviation. x1=∑x1n1=67.3210=6.732 x2=∑x2n2=32.98=4.1125s12=∑(x1-x1)2n1-1s12=79.160169=8.7956s22=∑(x2-x2)2n2-1s22=16.939557=2.4199 To test the hypothesis Ho:μ1=μ2 VS Ha:μ1>μ2 Given that Population variances are unequal. We used Unpooled t test. Test statistic t=x1-x2s12n1+s22n2t=6.732-4.11258.795610+2.41998t=2.61950.87956+0.3024875t=2.61951.1820475=2.409356t= 2.4094 Test statistic t=2.4094 To find degrees of freedom df= Smaller (n1-1, n2-1) df=Smaller(10-1, 8-1) df =7 To find p value p value = P(t> 2.4094) p value =0.0234 From Excel The correct decision is to reject the null hypothesis since p value < α=0.06 The correct summary : There is enough evidence to support the claim that sleeping with lights on can cause weight gain.