Hypothesis Test for μ (when σ is known)

 

Suppose that you want to determine if the average pH of a lake is less than neutral (7).

You know from past experience that the population standard deviation is 2. The data is

 7.8, 7.5, 7.4, 7.8, 6.9, 6.8, 6.5, 6.7, 6.9, and 6.3 So, Ho: μ = 7 versus Ha: μ < 7

When sigma is known, you want to conduct a HT that uses z.

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

  1. Enter the variable that you want and the known standard deviation.
  2. Enter the hypothesized value of mu as the test mean. (In this case, 7)
  3. Now click on Options.


 

  1. Do not worry about the blank for the confidence level.
  2. Next pick the alternative that matches your alternative hypothesis.
    1. If you want a two-sided test, select "not equal" as your alternative.
    2. If you want a one sided test, select "less than” or  "greater than".
  3. Your output should look like the output below.

 

One-Sample Z: C1

 

Test of mu = 7 vs < 7

The assumed standard deviation = 2

 

 

                                             95%

                                           Upper

Variable   N     Mean    StDev  SE Mean    Bound     Z      P

C1        10  7.06000  0.53166  0.63246  8.10030  0.09  0.538