Question

A consumer protection group randomly checks the volume of different beverages to ensure that companies are packaging the stated amount. Each individual volume is not exact, but a volume of iced tea beverages is supposed to average to 300 mL with a standard deviation of 3 mL. The consumer protection group sampled 20 beverages and found the average to be 298. 4 mL. Using the given table, which of the following is the most restrictive level of significance on a hypothesis test that would indicate the company is packaging less than the required average 300 mL? Upper-Tail Values a 5% 2. 5% 1% Critical z-values 1. 65 1. 96 2. 58 1% 2. 5% 5% 10%.

Answer 1

The level of significance that would indicate the company is packaging less than the required average and being most restrictive is $\alpha = 0.025 = 2.5\%$

How to form the hypotheses?

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

For this case, we have:

• Population mean = $\mu$ (not known, but want to check if its less than 300 mL)
• Population standard deviation = $\sigma = 3 \: \rm mL$
• sample size = $n = 20$
• sample mean = $\overline{x} = 298.4 \: \rm mL$

Hypotheses:

• Null hypothesis:  The company is packaging the required average or  $H_0: \mu = 300$
• Alternate hypothesis: The company is packaging less than the required average or $H_a: \mu < 300$

Since sample size = 20 < 30, thus, we will use t-test.

The value of t test statistic is calculated as:

$t = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}$

Thus, we get:

$t = \dfrac{298.4 - 300}{3/\sqrt{20}} \approx 2.385$

The degree of freedom is n - 1 = 20 - 1 = 19

The p-value for this is  0.0138 = 1.38%

This is less than 2.5%, 5% and 10% but bigger than 1%

For showing that company is manufacturing less than needed, we need p value to be smaller than level of significance, so that we can reject null-hypothesis and accept the alternate hypothesis.

Thus, only 2.5%, 5% and 10% as level of significance would be helpful.

Now, the most restricting one is 2.5% as it is closest to 1.38%.

Thus, the level of significance that would indicate the company is packaging less than the required average and being most restrictive is $\alpha = 0.025 = 2.5\%$

Learn more about t-test for single mean here:

https://brainly.com/question/25316952