9.5.2  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=[n_s,n_e] for the sample data information, where n_s is the the number of successes and n_e is the number of trials n_e.
    • 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