Finite Population:  Proportion

Problem:

Preethi limited likes to introduce a modern grinder. They have estimated that out of 14500 (N)people 40% (p) would buy the new grinder. Under the survey of 8500 people researchers found 4300 people were ready to buy the new grinder. In that 3000 people are still skeptical in buying the grinder. At 5% level of significance if the company can conclude that there is an increase in the interest in the new grinder

#solution

  • #Null hypothesis H0 p= 0.40 Population parameter
  • #Alternative hypothesis H1 p <> 0.40. Two tailed-test
  • #Significance level alpha = 0.05.
  • #Criterion: z(cal) must be > z(table) for rejecting Null Hypothesis
  • #proportion phat = 3000/8500 =0.353= phat
  • p= 0.40
  • phat = 0.353
  • q = 1-0.4
  • q =0.6
  • N = 14500
  • n = 8500
  • z = (phat-p)/(sqrt((p*q)/n)*sqrt((N-n)/(N-1)))
  •   = (0.353-0.40)/(sqrt(0.4*0.6)*sqrt(14500-8500)/(14500-1))
  • = (-0.047)/(0.0053*0.6432)
  • =-13.749

Since the abs(z) = 13.749 is greater than the abs(Z-Critical value) = 3.289 we reject the null hypothesis and accept the alternative hypothesis and conclude that the claim of 40% of people would buy the new grinder may not be true.

Using python:

Output:

Find z-calculated value using function:

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