# Testing the mean with the Z test: normalt

### 8.5.2 Testing the mean with the Z test: normalt

The normalt command uses the Z test to test the mean of data.

- normalt takes three mandatory arguments and one optional argument:
  - L, a list, which can be one of:
    - L=[ns,ne] for the sample data information, where ns is the the number of successes and ne is the number of trials ne.
    - L=[m,t], where m is the mean and t is the sample size.
    - L, a data list from a control sample.
  - σ, the standard deviation of the population. If the data list from a control sample is provided, then this argument is unnecessary.
  - test, the type of test, one of !=,< or >.
  - Optionally, c, the confidence level (by default 0.05).
- normalt(L,σ,test ⟨, c ⟩) returns the result of a Z test. It will return 0 if the test fails, 1 if the test succeeds, and it will display a summary of the test.

#### Examples.

- Input:
  normalt([10,30], 0.5, 0.02, ’!=’, 0.1)
  Output:

  `*** TEST RESULT 0 ***`
  `Summary Z-Test null hypothesis H0 mu1=mu2, alt. hyp. H1 mu1!=mu2.`
  `Test returns 0 if probability to observe data is less than 0.1`
  `(null hyp. mu1=mu2 rejected with less than alpha probability error)`
  `Test returns 1 otherwise (can not reject null hypothesis)`
  `Data mean mu1=10, population mean mu2=0.5`
  `alpha level 0.1, multiplier*stddev/sqrt(sample size)= 1.64485*0.02/5.47723`
  `0`

- Input:
  normalt([0.48,50],0.5,0.1,’<’)
  Output:

  `*** TEST RESULT 1 ***`
  `Summary Z-Test null hypothesis H0 mu1=mu2, alt. hyp. H1 mu1<mu2.`
  `Test returns 0 if probability to observe data is less than 0.05`
  `(null hyp. mu1=mu2 rejected with less than alpha probability error)`
  `Test returns 1 otherwise (can not reject null hypothesis)`
  `Data mean mu1=0.48, population mean mu2=0.5`
  `alpha level 0.05, multiplier*stddev/sqrt(sample size)= 1.64485*0.1/7.07107`
  `1`