Question

In an experiment, some diseased mice were randomly divided into two groups. One group was given an experimental drug, and one was not. The mean remaining lifespan of the mice given the drug was 18.2 days, and the mean remaining lifespan of those not given the drug was 15.9 days. The experiment was randomly simulated many times using a computer without knowing the effects of the drug, and the standard deviation of the differences of the sample means of the two groups was 1.1 days. Was the difference in the means in the actual experiment significant at a 95% confidence level, and for what reason?A)No, because the difference in the means in the actual experiment was less than two standard deviations from 0.B)No, because the difference in the means in the actual experiment was more than two standard deviations from 0.C)Yes, because the difference in the means in the actual experiment was less than two standard deviations from 0.D)Yes, because the difference in the means in the actual experiment was more than two standard deviations from 0.

Answer 1

Answer:

D)Yes, because the difference in the means in the actual experiment was more than two standard deviations from 0.

Step-by-step explanation:

We will test the hypothesis on the difference between means.

We have a sample 1 with mean M1=18.2 (drug group) and a sample 2 with mean M2=15.9 (no-drug group).

Then, the difference between means is:

$M_d=M_1-M_2=18.2-15.9=2.3$

If the standard deviation of the differences of the sample means of the two groups was 1.1 days, the t-statistic can be calculated as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{2.3-(0)}{1.1}=2.09$

The critical value for a two tailed test with confidence of 95% (level of significance of 0.05) is t=z=1.96, assuming a large sample.

This is approximately 2 standards deviation (z=2).

The test statistict=2.09 is bigger than the critical value and lies in the rejection region, so the effect is significant. The null hypothesis would be rejected: the difference between means is significant.