Hypothesis Test for μ (when σ is unknown and n<30)

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

 you do not know the population standard deviation. 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 unknown, and n<30, you want to conduct a hypothesis test that use t.

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

  1. Enter the hypothesized value of mu into the test mean blank.
  2. 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. You should get output similar to the output below.

Results for: Worksheet 1

 

One-Sample T: C1

 

Test of mu = 7 vs < 7

 

 

                                             95%

                                           Upper

Variable   N     Mean    StDev  SE Mean    Bound     T      P

C1        10  7.06000  0.53166  0.16813  7.36820  0.36  0.635