Hypothesis Testing continued2

SCENARIO

  • A retailer is selling Strawberries as 250 grams punnets
  • A shopper complains that the punnets weigh in less than 250 grams
  • Retailer decides to check a sample weight of 36 punnets. The average weight in this test was found to be 248.5 grams
  • If significance test is used, choose the outcomes below:
    • At 5% level he is selling underweight
    • At 5% level he is not selling underweight
    • At 5% level the test is inconclusive
    • A significance test cannot be made
SOLUTION

 Given:
n = 36, X-bar = 248.5, Sigma = 4.8
H0: Mu = 250
Ha: Mu < 250

Z = (248.5 - 250)/(4.8/SQRT(36)) = -1.875

On the negative side of the One tail test, Z-Critical(Z-c) = NORM.S.INV(0.05) = -1.645

CONCLUSION
  • Clearly, Z-c > Z. Thereby, we reject the NULL hypothesis
  • We conclude that the strawberry punnets are underweight

STATE NULL AND ALTERNATE HYPOTHESIS


  • Is the average waiting time for the customers at the checkout greater than 15 minutes?
    • H0: Mu <= 15
    • Ha: Mu > 15
    • One Tail Test on the positive side
  • Is the proportion of the households owning Color TV in Chennai less than 0.4?
    • H0: Probability >= 0.4
    • Ha: Probability < 0.4
    • Since Proportion is given, we understand the reference is Probability 
    • One Tail Test on the negative side
  • Is average expenditure of eating out higher in Bengaluru than Hyderabad?
    • H0: MuB <= MuH
    • Ha: MuB > MuH
    • One Tail Test on the positive side
  • Two random sample surveys is conducted within two months gap to access public opinion on - "Would you vote for or against the ruling party?"
    • H0: ProbabilityFirstMonth = ProbabilityThirdMonth
    • H1: ProbabilityFirstMonth <> ProbabilityThirdMonth
    • It is a Two Tailed Test
      • H0 = The proportion of the people in first month voting for the ruling party remains same even the third month
      • H1 = The proportion of the people in first month voting for the ruling party changes in the third month. H1 can be more or less when first is compared with third month survey
REFERENCES

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