Confidence Intervals for μ (when σ is known)

 

Suppose that you are creating a 95% confidence interval for the average pH of a lake.

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

When sigma is known, you want to conduct a confidence interval 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 C1 in the Samples in Columns box and the known standard deviation in the standard deviation box.
  2. Now click on Options.


 

  1. Make sure that you entered the correct confidence level.
  2. Next, pick the type of confidence interval or bound.
    1. If you want a confidence interval select, "not equal" as your alternative.
    2. If you want a confidence bound, select "less than" for a upper bound or "greater than" for an lower bound.
  3. Your output may look like the following.

 
  One-Sample Z: C1

 

The assumed standard deviation = 2

 

 

Variable   N     Mean    StDev  SE Mean        95% CI

C1        10  7.06000  0.53166  0.63246  (5.82041, 8.29959)