Question

Minute Maid states that a bottle of juice contains 473 mL. Consumer groups are interested in determining if the bottles contain less than the amount stated on the label. To test their claim, they sample 30 bottles. The sample mean was 472mL and the standard deviation is 0.2. What does mu represent here? Group of answer choices The average contents of all bottles of juice in the population, which is 472mL. The average contents of all bottles of juice in the sample, which is unknown. The average contents of all bottles of juice in the sample, which is 472mL. The average contents of all bottles of juice in the population, which is unknown.

Answer 1

Answer:

The average contents of all bottles of juice in the population

$\mu = 473\text{ mL}$

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =  473 mL

Sample mean, $\bar{x}$ = 472 mL

Sample size, n = 30

Sample standard deviation, s = 0.2

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 473\text{ mL}\\H_A: \mu < 473\text{ mL}$

Representation of $\mu$

• It is the population parameter for mean.
• Thus, it represents the average contents of all bottles of juice in the population, which is 473 mL.

Answer 2

The average juice a bottle contain is the mean value of the juice.

$\mathbf{\mu }$ is the average content in all bottles of juice in the population, which is 472mL.

The given parameters are:

$\mathbf{n = 30}$ --- the sample size

$\mathbf{\sigma = 0.2}$ --- the standard deviation

$\mathbf{\bar x = 472}$ --- the sample mean

$\mathbf{\mu = 473}$ --- the population mean

The above highlights means that:

The parameter $\mathbf{\mu }$ represents the population mean

This means that:

$\mathbf{\mu }$ is the average content in all bottles of juice in the population.

From the question, the value is given as: 473

Hence, the true statement is:

$\mathbf{\mu }$ is the average content in all bottles of juice in the population, which is 473mL.

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