a beverage bottling company labels a product as having a mean volume of 12 oz. it is important to the company and consumers that the volume of each beverage is as close to 12 oz as possible. a quality control analyst randomly selects 40 beverages and finds that the mean volume is 12.2 oz, and the standard deviation is 0.7 oz. the company will need to adjust the bottling procedures if evidence exists that the mean volume of all beverages differs from 12 oz. is this enough evidence at

The company needs to adjust the bottling procedures since p < α i.e., 0.0117 < 0.10. Using z-score test statistics, the required value is obtained.

What is Mean ?

The mean of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the “average.”

What is Deviation ?

Deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean.

How to calculate the z-score?

The z-score is calculated by

z = ( - μ)/(σ/√n)

Where :- sample mean; μ - population mean; σ - standard deviation; n - sample size.

It is given that,

Population mean μ = 12 oz

Sample size n = 40

Sample mean = 12.2 oz

Standard deviation σ = 0.7 oz

Constructing the test hypothesis as below:

H0: μ = 12 oz

Ha: μ < 12 oz (as close as possible)

Then, the z-score is

z = (12.2 - 12)/(0.7/√40)

= 0.2/0.1106

= 1.808

Thus, the required p-value for the obtained test score is p = 0.0117 from the distribution table.

Since p(0.0117) < 0.10(significance level), the null hypothesis is rejected.

Therefore, the company needs to adjust the bottling procedures since the mean volume of all beverages differs from 12 oz.

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