# Common test statistics

Step 1: State the Null hypothesis. The accepted fact is that the population mean is 100, so: H_{0}: μ=100.

Step 2: State the Alternate Hypothesis. The claim is that the students have above average IQ scores, so:

H_{1}: μ > 100.

The fact that we are looking for scores “greater than” a certain point means that this is a one-tailed test.

Step 3: Draw a picture to help you visualize the problem.

Step 4: State the alpha level. If you aren’t given an alpha level, use 5% (0.05).

Step 5: Find the rejection region area (given by your alpha level above) from the z-table. An area of .05 is equal to a z-score of 1.645.

Step 6: Find the test statistic using this formula:

For this set of data: z= (112.5-100) / (15/√30)=4.56.

Step 6: If Step 6 is greater than Step 5, reject the null hypothesis. If it’s less than Step 5, you cannot reject the null hypothesis. In this case, it is greater (4.56 > 1.645), so you can reject the null.

## One Sample Hypothesis Testing Examples: #3

Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A researcher thinks that a diet high in raw cornstarch will have a positive or negative effect on blood glucose levels. A sample of 30 patients who have tried the raw cornstarch diet have a mean glucose level of 140. Test the hypothesis that the raw cornstarch had an effect.

Step 1: State the null hypothesis: H_{0}:μ=100

Step 2: State the alternate hypothesis: H_{1}:≠100

Step 3: State your alpha level. We’ll use 0.05 for this example. As this is a two-tailed test, split the alpha into two.

0.05/2=0.025

Step 4: Find the z-score associated with your alpha level. You’re looking for the area in *one tail only*. A z-score for 0.75(1-0.025=0.975) is 1.96. As this is a two-tailed test, you would also be considering the left tail (z=1.96)

Step 5: Find the test statistic using this formula:

z=(140-100)/(15/√30)=14.60.

Step 6: If Step 5 is less than -1.96 or greater than 1.96 (Step 3), reject the null hypothesis. In this case, it is greater, so you *can* reject the null.