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)":
$$\begin{array}{l}
\begin{array} { l l }
\text { Low-Protein Diet}&\text { High-Protein Diet}\
101.3(20.6)&127.5(21.1)
\end{array}
\end{array}$$ Researchers want to know if the amount of protein in the rats' diet significantly affects their weight gain. Based on the data, what is the absolute numerical value of t statistic for the appropriate test?

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)":
$$\begin{array}{l}
\begin{array} { l  l  } 
\text { Low-Protein Diet}&\text { High-Protein Diet}\
101.3(20.6)&127.5(21.1)
\end{array}
\end{array}$$ Researchers want to know if the amount of protein in the rats' diet significantly affects their weight gain. Based on the data, what is the absolute numerical value of t statistic for the appropriate test?

Quizplus · Accepted Answer

The t statistic is calculated using the formula for two independent samples: $$t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$$ where $\bar{X}_1$ and $\bar{X}_2$ are the sample means, $s_1^2$ and $s_2^2$ are the sample variances, and $n_1$ and $n_2$ are the sample sizes for the two groups. Plugging in the given values: $\bar{X}_1 = 101.3$, $\bar{X}_2 = 127.5$, $s_1 = 20.6$, $s_2 = 21.1$, $n_1 = n_2 = 7$, we get $$t = \frac{101.3 - 127.5}{\sqrt{\frac{20.6^2}{7} + \frac{21.1^2}{7}}} \approx 2.35.$$