Question

A shipment of 1000 baby lab mice arrives at the animal care facility with a nominal weight of 10 g per mouse. A simple random sample of ? n mice is selected and weighed. The average weight of the sample is 9.7 g. From past shipments, it is known that the standard deviation of weight among mice is 2 g. The technician wishes to test the hypothesis that the average weight of the mice equals the nominal value versus the hypothesis that the mice are underweight at ?=0.05 α=0.05 . The ? P ‑value for the test was 0.047. Which of the given statements is correct? There is a 4.7% chance that the average weight from the sample would be 9.7 g or less if the nominal weight were correct. There is a 4.7% chance that the nominal weight of 10 g is more than the sample mean of 9.7 g. There is a 4.7% chance that the mice are underweight. 4.7% of mice are underweight.

Answer 1

Ho: mu = 10
Ha: mu < 10
It is a left-tailed one-sample t-test.

The p-value = 0.047 < 0.05, hence we can reject the null hypothesis.
P-value is the probability that the average weight from the sample would be 9.7g or less if the null hypothesis is true OR if the nominal weight were correct.

Hence, A) the first statement is correct which is, There is a 4.7% chance that the average weight from the sample would be 9.7 g or less if the nominal weight were correct.