# Null and Alternative Hypothesis for Filling Soft Drink Bottles

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 oz. of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine.

-To determine whether or not the machine is properly adjusted, the correct hypothesis is:

a) Ho: Î¼ < 12 H1: Îœ â‰¤ 12

b) Ho: Î¼ â‰¤ 12 H1: Î¼ >12

c) Ho: Î¼ â‰ 12 H1: Î¼ =12

d) Ho: Î¼ = 12 H1: Î¼ â‰ 12

-In order to test the following hypothesis at an 'a' level of significance

Ho: Î¼ â‰¤ 100 H1: Î¼ >100

-The null hypothesis will be rejected if the test statistic 'z' is:

a) â‰¥ Za

b) â‰¤ Za

c) < -Za

d) < 100.

https://brainmass.com/statistics/hypothesis-testing/null-alternative-hypothesis-filling-soft-drink-bottles-359345

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A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 oz. of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine.

-To determine whether or mot the machine is properly adjusted, the correct hypothesis is:

a) Ho: Î¼ < 12 H1: Î¼ â‰¤ 12

b) Ho: Î¼ â‰¤ 12 H1: Î¼ >12

c) Ho: Î¼ â‰ 12 H1: Î¼ =12

d) Ho: Î¼ = 12 H1: Î¼ â‰ 12

-In order to test the following hypothesis at an 'a' level of significance

Ho: Î¼ â‰¤ 100 H1: Î¼ >100

-The null hypothesis will be rejected if the test statistic 'z' is:

a) â‰¥ Za

b) â‰¤ Za

c) < -Za

d) < 100

Solution:

Since we are concerned with both over filling and under filling, we have a two-tailed test and the correct hypotheses are

d)

We have

From the alternative hypothesis, we see that we have a right-tailed test. So the null hypothesis will be rejected if the test statistic

Correct answer is a).

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