Infinite population where sample size is less than 30 and Population Standard Deviation is known

  • z-Distribution
  • Sample Size < 30;
  • Population STD is known;
  • Null Hyp = <SOME VALUE>
  • Alt Hyp  < <SOME VALUE>  Left tailed
  • Alt hyp  >  <SOME VALUE>  Right tailed
  • One-tailed test;

Problem :  Sample Size < 30 ,Population Std Is known.

You can use either Z-distribution or t-distribution formula

ABC limited assumes(hypothesis H0) the average life of printing press is 16500hours.

  1. the standard deviation is 2500 hours(population parameter)
  2. Sample size is 28 printing presses
  3. company finds sample means 14500 hours.
  4. Significance level 0.01 is expected

Question arises: if the company can conclude the average life of the press is less than 16500 hours

solution

  1. Null hypothesis H0 = 16500(mu) Population parameter
  2. Alternative hypothesis H1 < 16500 hours
  3. Significance level alpha = 0.01. for this z(table) = -2.3263
  4. Criterion: z(cal) must be > z(table) for rejecting Null Hypothesis
  5. Here Small Sample Size is < 30
  6. Population standard deviation (2500) is given
  7. Distribution could be Z-distribution or t_distribution

Abs(z)=4.2332 is greater than abs(z table value)=2.3263 we reject the null hypothesis

Using Python

Read data

  Calculate z  and p-value

Calculate z critical value or  refer the table for one tailed test

Display results:

z- calculated value using function:

Recommendation:

Both based on rejection rule and probability <0.01 we reject Null hypothesis

Since the abs( zcal) value is greater than abs( ztable) value we reject the null hypothesis and accept the alternative hypothesis and come to a conclusion that the average life of the press is always less than 16500 hours at Alpha=0.01