FINITE POPULATION WHERE SAMPLE SIZE IS LESS THAN 30 AND POPULATION STANDARD DEVIATION IS NOT KNOWN

  • Problem : Sample Size >30 and Population Standard Deviation is not known
  • Mean annual income of 495 employees (N) is claimed as Rs.4.465(in thousands).
  • Random sample selected from the population 495  are given below;
  • Sample size = 31 (n) greater than 30 – Z distribution to be applied
  • Sample mean = xbar = 4.1867
  • Sample std = 1.7473
  •  Population std is not known
  1. Choose appropriate hypothesis for testing if there is a significant difference in the mean annual income µ =4.465
  2. Significance level is 0.05 (5%)

 Find mean, variance and std of the given sample:                                  Find Standard Error with FPC 

Find Calculated z value

  • Abs(z) = 5.095 which is higher than the z critical value 1.96
  • we reject the Null hypothesis H0: µ= 4.465   and
  • accept the alternative hypothesis H1: µ<>4.465

Using Python:

 a) Load Libraries and read data

b) Statistics summary

c) Find mean, variance and std of sample

d) Find standard error/standard deviation of sample for finite population as  population standard deviation is unknown

e) Find calculated value of z

f) Find critical value of z when you want to have 95% confidential level with two-tailed test

g) Find p-value for the of z-statistic calculated:

h) Display results and Recommendation