Test Statistic (z vs. t)
• When population standard deviation is known, solve for z and use the z-table.
• When population standard deviation is unknown (s will be given), solve for t and use the t-table

p-value Approach
1. Solve for the test statistic (z or t) using your sample mean (x-bar)
2. Solve for the p-value using z
a. If z is positive, subtract the % below the z-score from 1 to get the p-value
b. If z is negative, keep the % below the z-score from the table as the p-value
c. In either case, if it is a two-tail test, multiply the p-value by 2
3. Solve for the p-value using t
a. Find the 2 values for area in the upper tail that your t-value is between, those values compose the range for your p-value
b. If it is a two-tail test, multiply the 2 numbers of the range by 2
4. Compare p-value with alpha (level of significance)
a. If p-value is > alpha then do not reject the null
b. If p-value is < alpha then reject the null

Critical Value Approach
1. For a one-tail test, find the z-score that has the significance level below it.
2. If the z-value of your sample mean (x-bar) is positive, then compare to the positive form of the critical value
3. If the z-value of your sample mean (x-bar) is negative, then compare to the negative form of the critical value
4. For a two-tail test, divide the significance level by 2 and then determine the z-values that have that percent above and below
5. If the z-value for your sample mean (x-bar) is less than the negative critical value, reject the null
6. If the z-value for your sample mean (x-bar) is more than the positive critical value, reject the null
7. If the z-value for your sample mean (x-bar) is within/between the positive and negative forms of the critical value, do not reject the null

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1. Consider a sample with data values of 8, 36, 14, 18, and 24. Compute the mean and median.


2. Consider a sample with data values of 15, 9, 14, 11, 19, 23, 20, and 8. Compute the 30th and 45th percentiles.


3. Consider a sample with data values of 6, 26, 46, 36, 16, 56, 76, and 66. Compute the first and third quartiles, then determine the interquartile range (IQR).


4. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the variance, standard deviation, and coefficient of variation.

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