Using the t-distribution, as we have the standard deviation for the sample, it is found that since the test statistic is less than the critical value for the right-tailed test, there is evidence to support the belief that the mean is less than 15. 25 ounces.
<h3>What are the hypothesis tested?</h3>
At the null hypothesis, it is tested if the mean is of 15.25 ounces, that is:
At the alternative hypothesis, it is tested if the mean is of less than 15.25 pounds, that is:
.
<h3>What is the test statistic?</h3>
The test statistic 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?</h3>
Considering a <em>left-tailed test</em>, as we are testing if the mean is less than a value, with 36 - 1 = <em>35 df and the standard significance level of 0.05</em>, it is found that the critical value is .
Since the test statistic is less than the critical value for the right-tailed test, there is evidence to support the belief that the mean is less than 15. 25 ounces.
More can be learned about the t-distribution at brainly.com/question/16313918