Testing the mean with the Z test

### 18.5.2 Testing the mean with the Z test

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

normalt([10,30],0.5,0.02,'!=',0.1)

*** 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 (cannot 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

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normalt([0.48,50],0.5,0.1,'<')

*** 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 (cannot 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

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