Hypothesis Test for μ (when σ is unknown)

Suppose that you want to determine if the average weight of Bears collected by Gary Alt as reported by the Readers Digest in 1979 is less than 200lbs.

This data set is located as a worksheet on the Minitab CD in the Students12 folder called Bears2. The population standard deviation is unknown.

Ho: μ = 200 Ho: μ < 200

When sigma is unknown, and n>30, you want to conduct a HT that uses z.

(You can also use the t distribution.)

1. Find the sample standard deviation by using the descriptive statistics command. In this case, s = 117.8.

2. To do this, enter your data into C1. Then go to Stat, Basic Statistics, 1 sample z.

3. Your screen should look like this.

4. Enter the variable that you want and enter the sample standard deviation 117.8 as an estimate of the population standard deviation.

5. Enter the hypothesized value of μ in your hypothesis statement.

6. Now click on Options.

7. Do not worry about the blank for the confidence level.

8. Next pick the alternative that matches your alternative hypothesis.

a. If you want a two-sided test, select "not equal" as your alternative.

b. If you want a one sided test, select "less than" or  "greater than".

9. Your output should look similar to the output below.

One-Sample Z: Weight

Test of mu = 200 vs < 200

The assumed standard deviation = 117.8

95%

Upper

Variable N Mean StDev SE Mean Bound Z P

Weight 50 202.840 117.801 16.659 230.242 0.17 0.568