Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the critical value method or the 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. 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.

Answer 1

n=8, =14, =0.01

calculate the sample mean and sample standard deviation for given data we get

sample mean () = 14.05

sample standard deviation (s)= 0.3464

the null and alternative hypotheses is

Ho: = 14
Ha: 14

Calculte test statistic

Test statistic: t = 0.408

calculate t critical values for two tailed test with =0.01 and df= n-1 = 7

we get

Critical values: t = ± 3.499

Critical values are = ( -3.499 , 3.499)

since test statistics do not lie within rejection region

Failed to reject Null hypothesis (Ho).

Conclusion:
There is sufficient evidence to support the claim that the mean weight of the cereal in its packets is 14 oz.