Using the t-distribution, as we have the standard deviation for the sample, it is found that since the absolute value of the test statistic is greater than the critical value for the two-tailed test, there is enough evidence to conclude that the sample does not come from a population whose mean is 1,600 hours.
<h3>What are the hypothesis tested?</h3>
At the null hypothesis, it is tested if the mean is of 1600 hours, that is:
At the alternative hypothesis, it is tested if the mean is different of 1600 hours, that is:
<h3>What is the test statistic?</h3>
It is given by:
The parameters are:
- is the sample mean.
- is the value tested at the null hypothesis.
- s is the standard deviation of the sample.
In this problem, the values of the parameters are:
Hence, the value of the test statistic is:
<h3>What is the decision rule?</h3>
Considering a two-tailed test, as we are testing if the mean is different of a value, with 100 - 1 = 99 df and a significance level of 0.01, the critical value is of .
Since the absolute value of the test statistic is greater than the critical value for the two-tailed test, there is enough evidence to conclude that the sample does not come from a population whose mean is 1,600 hours.
More can be learned about the t-distribution at brainly.com/question/13873630