Question

5) The net weights of potato chips actually vary slightly from bag to bag. A quality technician randomly selects 10 bags of chips and the net weights (in ounces) are 13.82, 13.85, 14.01, 14.03, 13.88, 14.02, 14.04, 13.84, 13.84, 13.89. Use a = 0.1. a. Check the claim that the net weight of each bag exceeds 13.86 ounces. (5 marks) b. For the hypothesis in a), how many measurements should be taken to have the probability of Type II error less than or equal to 0.05, when the net weight is 14.0? (4 marks)

Answer 1

a)

Ho :   µ =   13.86  
Ha :   µ >   13.86   (Right tail test)
          
Level of Significance ,    α =    0.100  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   0.0911  
Sample Size ,   n =    10  
Sample Mean,    x̅ = ΣX/n =    13.9220  
          
degree of freedom=   DF=n-1=   9  
          
Standard Error , SE = s/√n =   0.0911/√10=   0.0288  
t-test statistic= (x̅ - µ )/SE =    (13.922-13.86)/0.0288=   2.151  
          
          
p-Value   =   0.0300   [Excel formula =t.dist(t-stat,df) ]
Decision:   p-value≤α, Reject null hypothesis       
Conclusion: There is enough evidence to that net weight exceed 13.86

b)

Sample Size should be greater than 5 or more

  

Please let me know in case of any doubt.

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