The average weight of a package of rolled oats is supposed t

The average weight of a package of rolled oats is supposed to be at least 19 ounces. A sample of 18 packages shows a mean of 18.79 ounces with a standard deviation of 0.40 ounce.

a. At the 5 percent level of significance, is the true mean smaller than the specification? Clearly state your hypotheses and decision rule.

rejected the null hypothesis.

or

failed to reject the null hypothesis.

c. Use Excel to find the p-value. (Round your answer to 4 decimal places.)

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   u   <=   19
Ha:    u   >   19
          
As we can see, this is a    1   tailed test.  
          
Thus, getting the critical t,          
df = n - 1 =    17      
tcrit =    1.739606726      
          
Getting the test statistic, as          
          
X = sample mean =    18.79      
uo = hypothesized mean =    19      
n = sample size =    18      
s = standard deviation =    0.4      
          
Thus, t = (X - uo) * sqrt(n) / s =    -2.227386361      
          
Also, the p value is          
          
p =    0.019860623      
          
As p < 0.05, we   REJECT THE NULL HYPOTHESIS.      
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If alpha = 0.01 instead, we will FAIL to reject the null hypothesis, as p > 0.01.

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p =    0.019860623   [ANSWER]