A random sample of 25 rats was fed a diet for a period of 4 weeks. The weight gain (in grams) was recorded for each rat. The average weight gain was 16.4 with a corresponding standard deviation of 3.0.
The P-value for testing the claim that this diet would increase weight by at least 15 grams would be
A) 0.005
B) 0.003
C) 0.014
D) 0.135

Question

Quizplus · Accepted Answer

Since we want to test the claim that the diet would increase weight by at least 15 grams, this is a one-tailed test. We can use a one-sample t-test with the null hypothesis being that the population mean weight gain is less than or equal to 15 grams and the alternative hypothesis being that the population mean weight gain is greater than 15 grams.

We can calculate the t-statistic as follows:

t = (16.4 - 15) / (3 / sqrt(25)) = 4.33

Using a t-table with 24 degrees of freedom (since we have 25 observations), we can find the corresponding p-value to be approximately 0.014.

Since the p-value is less than the common alpha levels of 0.05 and 0.01, we can reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the diet would increase weight by at least 15 grams. Therefore, the best choice is C.

A Random Sample of 25 Rats Was Fed a Diet