Using the t-distribution, it is found that since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.
<h3>What are the hypothesis tested?</h3>At the null hypothesis, it is tested if the average is not less than 25, that is:
At the alternative hypothesis, it is tested if the average is less than 25, that is:
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.
- n is the sample size.
Considering the situation described, the values of the parameters are given as follows:
Hence the test statistic is:
t = -0.04
<h3>What is the p-value and the conclusion?</h3>Using a t-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -0.04, the p-value is of 0.4844.
Since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.
More can be learned about the t-distribution at brainly.com/question/13873630
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