Assume That a Simple Random Sample Has Been Selected from a Normally

question 20

Essay

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.
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. $$\begin{array} { l l l l l l l l } 14.6 & 13.8 & 14.1 & 13.7 & 14.0 & 14.4 & 13.6 & 14.2\end{array}$$ Test the claim at the 0.01 significance level.

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Definitions:

Mean

The average of a set of numbers, obtained by dividing the sum of the numbers by the count of numbers.

Normal Random Variable

A random variable that has a normal distribution, often used in statistics and probability theory.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values, indicating how much the values differ from the mean of the set.

Mean

The arithmetic average of a data set, obtained by adding all the numbers and dividing by the count of numbers.