![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=3ef51f5420fdbb96775dda47f2de9e51.png\")
. Step 1:
\(1)
\A cereal company claims that the mean weight of the cereal in its packets is 14oz.
\Null hypothesis :
\One of these statements must become the null hypothesis , and the other should be the alternate hypothesis.
\The null hypothesis contains equality.
\So for the above, the null hypothesis H0 : x = 14.
\Step 2:
\Alternate hypothesis :
\The statement that does not contain equality is the alternative hypothesis.
\A cereal company claims mean weight which is not equal to 14oz.
\So for the above, the alternate hypothesis Ha : x ≠ 14.
\Step 3:
\Find the test statics.
\The sample size of the cereal packets is 7.
\Sample contains cereal packets of weights : 14.6, 13.8, 14.1, 13.7, 14.0, 14.4, 13.6.
\Calculate mean and standard deviation of the sample.
\Follow these steps to evaluate Mean and standard deviation.
\1.First enter the sample values.
\[STAT --> 1 --> L1 ]
\Enter the values in the L1 column.
\2.Select 1-variable stats
\[STAT --> Right navigation key --> ENTER]
\Var list L1.
\3.Now press Enter in calculator to view answer.
\Mean = 14.02857
\Standard deviation = 0.36839.
\Test static : .
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=50daa184b41bb5a39dfcf3039098f97d.png\")
Test statics : ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=894a5d56a2a73d80c64f31f309116efd.png\")
.
Step 4:
\Find the critical values.
\Significance value is 0.01.
\![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=1baade577cdd70a7c658f99ad77e1291.png\")
.
The sample size of the cereal packets is 7.
\Degree of freedom ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=c2f99f0f069205ab08c9646bceb4018a.png\")
.
Calculate the critical values using calculator.
\Follow these steps to evaluate critical values.
\1.Select invT()
\[2nd --> VARS --> 4 ]
\2.Enter the values of ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=04bc7530c7f1115d3df224f3ab774855.png\")
and df.
area : 0.01
\df : 6
\3.Now press Enter in calculator to view answer.
\invT(0.01, 6)
\=-3.14266.
\Step 5:
\Find the p-value.
\Follow these steps to evaluate p-value.
\1.Select tcdf()
\[2nd --> VARS --> 6 ]
\2.Enter the values of t and df.
\Lower : 0.20518
\Upper : 1000
\df : 6
\For two-tailed (non-directional), the upper value is considered as 1000.
\3.Now press Enter in calculator to view answer.
\tcdf(0.20518, 1000, 6)
\=0.4221
\p-Value of the hypotheses is 0.4221
\Step 6:
\Conclusion:
\Since the value of test statics is less than critical values, it fails to reject H0.
\The test results support the company claim.