A study examined the effect of protein consumption on weight gain in rats. Investigators obtained 14 female rats and randomly assigned 7 of them to a low-protein diet and the other 7 in a high-protein diet. After 60 days, the weight gained by each rat was recorded (in grams) . Here are the summary findings, displayed as "mean (standard deviation) ":
$\begin{array}{l}\begin{array} { l l } \text { Low-Protein Diet}&\text { High-Protein Diet}\\101.3(20.6) &127.5(21.1) \end{array}\end{array}$ Given that the degrees of freedom for the appropriate t procedure is approximately 12, what is a 95% confidence interval for ?_High - ?_Low?

Question

A study examined the effect of protein consumption on weight gain in rats. Investigators obtained 14 female rats and randomly assigned 7 of them to a low-protein diet and the other 7 in a high-protein diet. After 60 days, the weight gained by each rat was recorded (in grams) . Here are the summary findings, displayed as "mean (standard deviation) ":

\begin{array}{l}\begin{array} { l l } \text { Low-Protein Diet}&\text { High-Protein Diet}\\101.3(20.6) &127.5(21.1) \end{array}\end{array}

Given that the degrees of freedom for the appropriate t procedure is approximately 12, what is a 95% confidence interval for ?_High - ?_Low?

Quizplus · Accepted Answer

The 95% confidence interval for the difference in means between the high-protein and low-protein diets is calculated using the formula for two independent samples. Given the means and standard deviations, and knowing the degrees of freedom is approximately 12, the correct interval would account for the variability and the difference in means. Option A, 1.9 to 50.5 grams, is the only interval that makes sense in this context, as it reflects a range of possible differences between the two diet groups' weight gains, considering the given summary statistics.