Infinite Population where sample size is greater than 30 and Population standard deviation is not known

Problem :

Data X

  1. Sample size n = 31
  2. Population standard deviation is not known

Solution:

1. Find mean of the sample

  mean of the sample is 82.26

2. Find out standard deviation of the sample:

Here standard deviation of population is not given. σ is unknown

  a) Find Sample Standard Deviation:                                  b) Find  Z calculated value

                                         

Using Python:

1. Read data and find z calculated value

2. Find z-Critical value for the confidential level 5% (alpha = 0.05)-TWO-TAILED test

For 95% confidential level Z critical value will be 1.96

3. Report:

4. Recommendation:

  1. Abs(Z)= 1.419  value is less than abs(Z critical value) 1.96  we accept the Null hypothesis.
  2. Probability value (1.844) > 0.05  we accept the null hypothesis.