Suppose that the average grade for all people who take this course in statistics is 83 with a standard deviation of 3.5. If your particular class has an average of 89, can you conclude that your class is better than average at the 90 percent confidence level? Label and describeeach step of the hypothesis testing procedure, and be sure to specify whether this is a one-tailed or two-tailed test.
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n-1)
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.
To determine whether your class is better than average at the 90 percent confidence level, we can conduct a hypothesis test.
Step 1: State the null and alternative hypotheses:
- Null hypothesis (H0): The average grade of your class is not significantly different from the average grade of all people who take the course in statistics.
- Alternative hypothesis (HA): The average grade of your class is significantly higher than the average grade of all people who take the course in statistics.
Step 2: Determine the test statistic:
Since you have the sample average (89), the population average (83), and the standard deviation (3.5), we can use the Z-test. The formula for the Z-test is:
Z = (sample average - population average) / (standard deviation / sqrt(sample size))
Step 3: Determine the significance level and critical value:
Since the confidence level is 90%, the significance level (alpha) is 1 - confidence level = 1 - 0.90 = 0.10. To find the critical value, we need to use a Z-table or a statistical software. For a one-tailed test (since we are checking if your class is better than average), we will look at the upper tail of the distribution at the 10% level of significance.
Step 4: Calculate the test statistic:
Using the Z-test formula, we can plug in the values:
Z = (89 - 83) / (3.5 / sqrt(sample size))
Step 5: Compare the test statistic with the critical value:
If the test statistic is greater than the critical value, we reject the null hypothesis. If it is not, we fail to reject the null hypothesis.
Step 6: Make the decision and conclusion:
If the test statistic is greater than the critical value, we conclude that your class is better than average at the 90 percent confidence level. If the test statistic is not greater than the critical value, we fail to reach that conclusion.