Chapter 8, Section 2, Exercise 048 Light at Night Makes Fat Mice, Continued A st
ID: 3376571 • Letter: C
Question
Chapter 8, Section 2, Exercise 048 Light at Night Makes Fat Mice, Continued A study has shown that even low-level light at night can interfere with normal eating and sleeping cycles for mice. In the study, mice were randomly assigned to live in one of three light conditions: LD had a standard light/dark cycle, LL had bright light all the time, and DM had dim light when there normally would have been darkness. We have found that the groups had significantly different weight gain and time of calorie consumption. We can now explore these topics further. When Calories Are Consumed Researchers hypothesized that the increased weight gain seen in mice with light at night might be caused by when the mice are eating. Computer output for the percentage of food consumed during the day (when mice would normally be sleeping) for each of the three light conditions is shown, along with the relevant ANOVA output. Which light conditions give significantly different mean percentage of calories consumed during the day? Level Mean StDev 10 55.516 10.881 9 36.485 7.978 9 76.573 9.646 DM LDExplanation / Answer
Solution
Back-up Theory
To test the equality of two population means, say
Null: H0: µ1 = µ2 Vs Alternative: HA: µ1 ? µ2
Test Statistic is:
t = (Xbar - Ybar)/[s?{(1/n1) + (1/n2)}] where
s2 = {(n1 – 1)s12 + (n2 – 1)s22}/(n1 + n2 – 2);
Xbar and Ybar are sample averages and s1, s2 are sample standard deviations based on n1 observations on X and n2 observations on Y respectively.
Decision Criterion (Rejection Region):
Reject H0 if | tcal | > tcrit or p-value < ?
Now to work out the solutions,
Preparatory Work
Case
DM vs LD
DM vs LL
LD vs LL
n1 =
10
10
9
n2 =
9
9
9
Xbar =
55.56
55.56
36.485
Ybar =
36.485
76.573
76.573
s1 =
10.881
10.881
7.978
s2 =
7.978
9.646
9.646
s^2 =
92.63255
106.4664
78.3469
s =
9.62458
10.31825
8.851378
tcal =
10.10337
9.42414
6.831984
p-value =
1.33E-08
3.67E-08
4.03E-06
Part (a) DM vs LD
| t | = 10.10
p-value = 1.33E -08
Decision: Reject H0
Conclusion: There is evidence of a difference in means between the two light conditions.
DONE
Part (b) DM vs LL
| t | = 9.42
p-value = 3.67E -08
Decision: Reject H0
Conclusion: There is evidence of a difference in means between the two light conditions.
DONE
Part (c) LD vs LL
| t | = 6.83
p-value = 4.03E -06
Decision: Reject H0
Conclusion: There is evidence of a difference in means between the two light conditions.
DONE
Case
DM vs LD
DM vs LL
LD vs LL
n1 =
10
10
9
n2 =
9
9
9
Xbar =
55.56
55.56
36.485
Ybar =
36.485
76.573
76.573
s1 =
10.881
10.881
7.978
s2 =
7.978
9.646
9.646
s^2 =
92.63255
106.4664
78.3469
s =
9.62458
10.31825
8.851378
tcal =
10.10337
9.42414
6.831984
p-value =
1.33E-08
3.67E-08
4.03E-06
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