Using the t-distribution, as we have the standard deviation for the samples, it is found that since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the treatment increases the survival time of patients.
<h3>What are the hypothesis tested?</h3>
At the null hypothesis, we test if the treatment did not increase the survival time, that is, the subtraction of means is 0, hence:
At the alternative hypothesis, we test if the treatment has increased the survival time, hence:
<h3>What is the distribution of the differences of means?</h3>
For each sample, we have that:
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Hence, for the distribution of differences, the mean and the standard error are given by:
<h3>What is the test statistic?</h3>
It is given by:
In which is the value tested at the null hypothesis.
Hence:
<h3>What is the decision?</h3>
Considering a<em> right-tailed test</em>, as we are testing if the mean is greater than a value, with a <em>standard significance level of 0.05 and 8 + 8 - 2 = 14 df</em>, we have that the critical value is of .
Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the treatment increases the survival time of patients.
More can be learned about the t-distribution at brainly.com/question/13873630