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?

Identify one or two-tailed
States the Null and Alternative Hypothesis
States the Level of Significance
Calculates Test Statistic
Formulates Decision Rule
Makes a Conclusion

You need to consult your statistics text for the methods involved. However, I will start you out.

Since you are only concerned with whether the class (mean 2) scored higher, it is a one-tailed test.

Ho: mean 1 = mean 2
H1: mean 1 < mean 2

I'll leave the rest to you.

To determine whether your class is better than average at the 90 percent confidence level, we need to perform a hypothesis test.

One-Tailed or Two-Tailed Test:
Since we are only evaluating whether your class is better than average, we will conduct a one-tailed test.

Null and Alternative Hypothesis:
The null hypothesis (H0) states that your class is not better than average and the alternative hypothesis (Ha) states that your class is better than average.

H0: μ = 83 (average grade of the population)
Ha: μ > 83

Level of Significance:
The level of significance (α) defines the probability of rejecting the null hypothesis when it is true. In this case, the level of significance is 0.10 or 10% (90 percent confidence level).

Calculating the Test Statistic:
To calculate the test statistic, we use the formula for a z-score:
z = (x̄ - μ) / (σ / sqrt(n))

Where:
x̄ = sample mean (average grade of your class)
μ = population mean (average grade of all people who take the course)
σ = population standard deviation
n = sample size (number of students in your class)

In this case:
x̄ = 89
μ = 83
σ = 3.5 (provided)
n = [you need to specify]

Formulating the Decision Rule:
In a one-tailed test, the decision rule is based on critical values from the standard normal distribution. Since the alternative hypothesis states that your class is better than average, we will compare the test statistic to the critical value from the upper tail of the distribution.

The critical value can be found using a z-table or a statistical calculator, depending on the desired level of significance (α) and whether the test is one-tailed or two-tailed.

Making a Conclusion:
If the test statistic falls beyond the critical value in the rejection region, we reject the null hypothesis. This indicates that your class is significantly better than the average at the specified level of confidence. If the test statistic does not fall beyond the critical value, we fail to reject the null hypothesis, meaning there is not enough evidence to conclude that your class is better than average.

Note: Since you did not provide the sample size (n) of your class, you need to specify it in order to complete the calculations and make a final conclusion.