PROPORTIONS: INFINITE POPULATION

Problem

Preethi limited likes to introduce a modern grinder. In the survey of 10000 people researches found 4300 people were ready to buy the new grinder. Extensive study revealed that 6% of the people would buy the new 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= 0.06 Population parameter
  • Alternative hypothesis H1 p ≠ 0.06. Two tailed test
  • Significance level alpha = 0.05.
  • Criterion: z(cal) must be > z(table) for rejecting Null Hypothesis
  • P-value must be < 0.05 for rejecting null hypothesis
  • proportion phat = 4300/10000 =0.43
  • p =0.06
  • q = 1-p = 1-0.06 =0.94
  • phat = 0.43
  • n = 10000
  • z = (0.43-0.06)/sqrt((0.06*0.94)/10000)
  •   =0.37 /0.00237
  • = 155.7981

Abz(z)  calculated value 155.7981 is greater than abs(z-critical value)  (-3.2897)   we reject the Null hypothesis and accept the alternative hypothesis stating that the hypothesized proportion is not equal to 0.06.  the percentage of people that would buy the new grinder claimed may not be equal to 6%

using python:

Find Z-critical value:

Output:

Find Z-critical value using function:

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