Question

Suppose it is known from experience that the standard deviation of the weight of 10-ounce packages of cookies is 0.20 ounces. To check whether the true average is, on a given day, 10 ounces, employees select a random sample of 36 packages and find that their mean weight is x¯ = 9.45 ounces. Perform a two-tailed z-test on this data, checking at the α = .01 significance level

State the null hypothesis in writing and in numbers

State the alternative hypothesis in writing and numbers

Draw the distribution and label it appropriately

Define the critical values

Calculate the test statistic

Make your decision

Write out your answer

Answer 1

Ho :   µ =   10  
Ha :   µ ╪   10   (Two tail test)
          
Level of Significance ,    α =    0.010  
population std dev ,    σ =    0.2000  
Sample Size ,   n =    36  
Sample Mean,    x̅ =   9.4500  
          
'   '   '  

critical z value, z* =   ±   2.5758   [Excel formula =NORMSINV(α/no. of tails) ]
          
Standard Error , SE = σ/√n =   0.2/√36=   0.0333  
Z-test statistic= (x̅ - µ )/SE =    (9.45-10)/0.0333=   -16.500  
          

  Decision: |TEST STAT| > |CRITICAL VALUE| Reject null hypothesis

THERE IS SUFFICIENT EVIDENT TO SAY THAT WEIGHT OF 10-ounce packages of cookies is different than 10

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