Question

A shipment of 1000 small lab mice arrives at the animal care facility. We wish to estimate the actual mean weight of the mice. A simple random sample of 100 mice is selected and weighed, and the resulting 95% confidence interval for the actual mean weight is from 9.9 to 10.5 gram. Using the same data to test the hypotheses about the actual mean weight, which of the following is correct? We cannot reject the hypothesis that the sample mean is 10.2 gram at α = 0.05 We cannot reject the hypothesis that 95% of individual mice weight between 9.9 and 10.5 gram We can reject the hypothesis that the true mean is 10 gram at α = 0.05 We can reject the hypothesis that the true mean weight is 11 g versus that the mean weight is not equal to 11 gram at α = 0.05

Answer 1

• We cannot reject the hypothesis that the sample mean is 10.2 gram at α = 0.05

• We can reject the hypothesis that the true mean weight is 11 g versus that the mean weight is not equal to 11 gram at α = 0.05

Explanation:

We cannot reject the hypothesis that the sample mean is 10.2 gram at α = 0.05

True . Given the confidence interval from 9.9 to 10.5 gram, we can conclude that true population mean can be estimated 10.2±0.3 in 95% confidence.

We cannot reject the hypothesis that 95% of individual mice weight between 9.9 and 10.5 gram

False. Confidence interval is an estimation about the population mean, not about the indivudual samples.

We can reject the hypothesis that the true mean is 10 gram at α = 0.05

False. We cannot reject this hypothesis sice 10 gram is in the confidence interval at 0.05 significance

We can reject the hypothesis that the true mean weight is 11 g versus that the mean weight is not equal to 11 gram at α = 0.05

True. According to the sample results 11 gram is out of the confidence interval in 95 confidence level. Therefore we can reject the hypothesis that true mean weight is 11 g.