FINITE POPULATION WHERE SAMPLE SIZE IS GREATER THAN 30 AND POPULATION STANDARD DEVIATION IS KNOWN

  1. Sample Size > 30;
  2. Population STD is known;
  3. Null Hyp =
  4. Alt Hyp ≠;
  5. Two-tailed test;
  6.  Z-Distribution

Problem : Sample size >30 and Population Standard deviation is known

Theatre owners in Tamil Nadu know that a hit film ran for an average of 84 days µ(µ) with a standard deviation of 10 days (σ) in each city. Total theatres in Tamil Nadu works out to 500. One film distributor wanted to compare the popularity of the film in his region with that of population parameter in Tamil Nadu. He selected 75 theatres in his region and found the popular move ran for 81.5 days(xbar)

  1. Choose appropriate hypothesis for testing if there is a significant difference in the distributor region and the population
  2. Significance level is 0.01 (1%)

Given:

  1. #Finite population
  2. #total population 500 (N)
  3. #selected theatre 75    (Sample size n)
  4. #Null hypothesis H0 = 84(mu) Population parameter
  5. #Alternative hypothesis H1 not equal to  84 days
  6. #Significance level alpha = 0.01. for this ztab # need two-tailed test
  7. #Criterion: z(cal) must be > z(table) for rejecting Null Hypothesis
  8. #sample size = 75  theatres
  9. #Specific value 81.5 xbar (sample mean)
  10. #Here sample size is >30
  11. #Population standard deviation (10 days) is given σ p
  12. #Distribution could be z-distribution
  13. #Null hypothesis H0 : µ = 84
  14. #Alternative hypothesis H1 : µ<>84

Solution

  • Based on Z calculated and Z critical value
  • Abs(z) value 0.2459 is less than abs( Z critical value) 2.546 we accept null hypothesis as we do not have sufficient evidence to reject null hypothesis
  • Based on probability
  • If calculated probability is > 0.01 Reject null hypothesis
  • If calculated probability is < 0.01 Accept null hypothesis

Using Python:

Load libraries and read data

Calculate Standard Error of mean distribution with finite population correction 

Calculate p-value using function:

Calculate z-critical value using function:

Display results:

Find z-Calculated value using function

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