Assume that a simple random sample has been selected from a normally distributed

Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. 6) A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below. 14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2 Test the claim at the 0.01 significance level.

Explanation / Answer

Null, H0: U=14
Alternate, H1: U!=14
Test Statistic
Population Mean(U)=14
Sample X(Mean)=14.05
Standard Deviation(S.D)=0.3464
Number (n)=8
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =14.05-14/(0.3464/Sqrt(8))
to =0.408
| to | =0.408
Critical Value
The Value of |t | with n-1 = 7 d.f is 3.499
We got |to| =0.408 & | t | =3.499
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 0.4083 ) = 0.6953
Hence Value of P0.01 < 0.6953,Here We Do not Reject Ho

We have evidence to indicate that claims that the mean weight of the cereal
in its packets is 14 oz.

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