A study was introduced that examined the effect of light at night on weight gain

Question

A study was introduced that examined the effect of light at night on weight gain in mice. In the full study of 27 mice over a four-week period, the mice who had a light on at night gained significantly more weight than the mice with darkness at night, despite eating the same number of calories and exercising the same amount. Researchers noticed that the mice with light at night ate a greater percentage of their calories during the day (when mice are supposed to be sleeping). The computer output shown below allows us to examine the relationship between percent of calories eaten during the day, DayPct, and body mass gain in grams, BMGain. A scatterplot with regression line is also shown below. Pearson correlation of BMGain and DayPct 0.740 P-Value-0.000 The regression equation is BMGain.0.127 DayPct PredictorCoef SE Coef TP Constant 3 .382 0.81 0.428 DayPct 0.12727 0.02315 5.50 0.000 S-2.23097 R-Sq-54.7% R-Sq (adj)-52.9% 18 16 14 12 10 21- 2030405060708090 DayPct

Explanation / Answer

(a) Yes, the answer is correct/

(b) The correlation is 0.740

the p - value is 0.000.

Accept H0.

(c) Here the linear regression equation is

y^ = 1.113 + 0.12727 * DayPct

where Daypct = 51%

y^ = 1.113 + 0.12727 * 51 = 7.6038 grams

(d) Here slope = 0.12727 grams/percent gains incalorie

Here if we increase the value of Daypct by 1 gm then it will increase the value of BM(gain) by 0.12727 gm

(e) The p - value = 0.000

Reject H0.

(f) Here the p-value are the same for both the test.

(g) R2 = 0.547

here the interpreation of R2 is that 54.7% variability in BM gain is explained by variability in Daypct.

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