Question

A coffee machine is supposed to dispense 8 ounces (oz) of coffee into a paper cup. In reality, the amounts dispensed vary from cup to cup. However, if the machine is working properly, the standard deviation of the amounts dispensed should be less than 0.3/0.4/0.5 oz. To test this, a random sample of 10/15/20 cups was taken, and it give a standard deviation of 0.255 oz.

a)     At the 5% significance level, do the data provide sufficient evidence to conclude that the standard deviation of the amounts being dispensed is less than 0.3/0.4/0.5 oz?

b)    Why is it important that the standard deviation of the amounts of coffee being dispensed not be too large?

Answer 1

a)

Ho :   σ =   0.255
Ha :   σ <   0.255
      
Level of Significance ,    α =    0.05
sample Std dev ,    s =    0.345
Sample Size ,   n =    10
      
Chi-Square Statistic   X² = (n-1)s²/σ² =    16.474
      
degree of freedom,   DF=n-1 =    9
      
one tail test       
lower critical value   =   3.325112843
p-value   =   0.942381717
      
Do not reject the null hypothesis      

data provide sufficient evidence to conclude that the standard deviation of the amounts being dispensed is less than 0.345

b)

Large standard deviation will give the results in large range and hence it could be possible that coffee machine can dispense coffee very large amountts to small amounts. We want it to always around 8 ounces

THANKS

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