A machine that is programmed to package 2.40 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 29 cereal boxes, the mean and standard deviation are calculated as 2.44 pounds and 0.17 pound, respectively. Use Table 2. 
a. 
Select the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either underfilling or overfilling the cereal boxes. 


b. 
Calculate the value of the test statistic. (Round your answer to 2 decimal places.) 
Test statistic 
c1.  Approximate the pvalue.  

c2.  What is the conclusion at the 1% significance level?  

d1.  Calculate the critical value(s) at a 1% level of significance. (Round your answer to 3 decimal places.) 
Critical value(s)  ± 
d2.  Can you conclude that the machine is working improperly?  

Solution:
a)
H_{0}: µ = 2.40; H_{A}: µ ≠ 2.40
b)
The test statistic t is
t = (  )/[/n] = [2.44  2.40]/[0.17 /29] = 1.27
Test statistic : 1.27
c1)
d.f. = n  1 = 29  1 = 28
Two tailed test
t = 1.27
Using t table ,
0.20< pvalue < 0.40
c 2)
Do not reject H_{0} since the pvalue is greater than α.
d 1)
= 1% =0.01
/2 = 0.005
Two tailed test
So , critical values are
Critical value(s) : 2.763
d 2)
No
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