Question

6. A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink as specified on the bottle labels. Any overfilling or underfilling results in the shutdown and readjustment of the machine.  A sample of 64 bottles was taken and their contents measured to test whether the machine was operating properly. The sample mean was 11.8 ounces and the estimated population standard deviation was 1.5 ounces.

1. Formulate the hypotheses in words and in symbols.
2. Is this an upper-tailed test, lower-tailed test, or a two-tailed test?
3. Compute the value of the test statistic (i.e. the z-score)
4. Compute the p-value
5. Determine whether to reject the null hypothesis given a level of significance (alpha) of .05
6. Based upon your decision in “d” above, what is your conclusion regarding the machine’s operations?

Answer 1

Solution:

Given:   A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink as specified on the bottle labels. That is:

Sample size = n = 64

Sample mean =

The estimated population standard deviation =

Any overfilling or underfilling results in the shutdown and readjustment of the machine.

This statement is two sided, thus this is two tailed test.

Part a) Formulate the hypothesis in words and in symbols.

H0: A juice drink filling machine fills the bottles with 12 ounces of drink

Vs

H1: A juice drink filling machine fills the bottles different from 12 ounces of drink.

Vs

Part b) Is this an upper-tailed test, lower-tailed test, or a two-tailed test?

Two tailed test

Part c) Compute the value of the test statistic (i.e. the z-score)

Part d) Compute the p-value

For two tailed test , p-value is:

p-value = 2* P(Z > z test statistic) if z is positive

p-value = 2* P(Z < z test statistic) if z is negative

thus

p-value = 2* P(Z < z test statistic)

p-value = 2* P(Z < -1.07)

Look in z table for z = -1.0 and 0.07 and find corresponding area.

P(Z < -1.07) = 0.1423

thus

p-value = 2* P(Z < -1.07)

p-value = 2* 0.1423

p-value = 0.2846

Part e) Determine whether to reject the null hypothesis given a level of significance (alpha) of .05

Decision Rule:
Reject null hypothesis H0, if P-value < 0.05 level of significance, otherwise we fail to reject H0

Since p-value = 0.2846 > 0.05 level of significance, we fail to reject H0

Part f) Based upon your decision in “d” above, what is your conclusion regarding the machine’s operations?

At 0.05 level of significance, we conclude that: a juice drink filling machine, fills the bottles with 12 ounces of drink as specified on the bottle labels. So there is no need of readjustment of the machine.