## Question 838:

1

No answer provided yet.Below are the five-steps to conduct a hypothesis test to determine if there is a statistical difference.

Step 1: The Null Hypothesis is that the population mean is not different than 25. The alternative hypothesis is that the population mean differs from 25.

Step 2: We will perform a 1-sample t-test on the data since we don't know the population standard deviation.

Step 3: We will reject the Null Hypothesis is the p-value is less than the alpha value of .05.

Step 4: The 1-sample t-test is calculated using the following steps.
1. Subtract the sample mean from the test mean = 25-24  = 1.
2. Divide the difference between the means by the standard error of the mean (SEM). The SEM is found as the standard deviation divided by the square root of the sample size = 10/SQRT(400) = .5.
3. The test statistic is then 1/.5 = 2.
4. To generate a p-value from this test statistic we lookup the 2-sided value in a t-table using n-1 degrees of freedom (399) and get the p-value of  .046.
Step 5: Since the p-value obtained of .046 is less than the alpha cut-off value of .05 we reject the Null Hypothesis. We conclude that there is sufficient evidence (beyond chance fluctuations) that the population mean is different than 25.