Question

8) A scientific supply company has developed a new breed of lab rat, which it claims weighs the same as the classic white rat. The population mean (and standard deviation) for the classic white rat is 485 grams (20 grams). A researcher obtained a sample of 76 of the new breed of rats, weighed them, and found M = 500 grams (SD = 12 grams). What test should he do to see if the company’s claim is true? Complete the test necessary to examine the claim of the scientific supply company (α = .05), and write the results in APA format.

Answer 1

Aim: The aim is to test whether the lab rats weigh same as the classic white rats.

Appropriate test: The appropriate test is the t-test for mean as the population standard deviaiton is not known for the lab rats.

Null hypothesis: H₀: The true mean weight of the lab rats is same as the true mean weight of the classic white rat.

Alternate hypothesis: H₁: The true mean weight of the lab rats is not same as the true mean weight of the classic white rat.

Test statistic:

Assumptions:

i) The samples are random and independent.

ii) The samples are drawn from normal population.

Observed test statistic:

Level of significance and p-value:

The level of significance is 0.05 and the p-value for the observed test statistic can be found as

2P(t₇₅ < 10.897) < 0.05

Conclusion:

The t-test conducted for testing the population mean of lab rats gave test statistic as 10.897, p value < 0.05. So there is sufficient evidence to reject the null hypothesis at 5% level of significance and it is reasonable to conclude that the weight of the lab rats differ from the weight of the classic white rat. The claim of the scientific supply company is not valid.