Question

Many fast-food restaurants use automatic soft-drink dispensing machines that fill cups once an order is placed at a drive-through window. A regional manager for a fast-food chain wants to determine if the machines in her region are dispensing the same amount of product. She samples four different machines and measures a random sample of 16-ounce drinks from each machine. Here is the data she collects (in ounces):

Machine 1	Machine 2	Machine 3	Machine 4
16.5	15.0	16.0	16.6
16.6	15.4	16.3	15.9
16.5	15.3	16.5	15.5
15.8	15.7	16.4	16.2
15.6	15.2	17.3	17.0
16.4	16.0	16.7	15.5
16.1	15.6	15.7	16.3

a) “Number of ounces” is a quantitative variable. Is it discrete or continuous?

b) “Number of ounces” is what level of measurement?

c) Is this a designed experiment or an observational study? Briefly explain.

d) At the 5% Level of Significance, determine whether or not the data indicate that the mean amount dispensed from the machines is not the same, by doing each of the following:

            1) Write the Hypotheses.

2) Use your calculator to do a one-way ANOVA test. Explain in some detail how the results of the test lead you to reject or not reject the null hypothesis.

3) Write a formal conclusion.

e) Using the language of our textbook on bias, name at least one type of bias that might be present in this research. Briefly explain.

Answer 1

a) Discrite as it is countable.

b) It is interval level of measurement.

c) It is observational study.

d)

1) Null Hypothesis H0 : M1 = M2 = M3 = M4

Alternative Hypothesis Ha : M1 M2 M3 M4

2)

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Machine 1	7	113.5	16.21429	0.151429
Machine 2	7	108.2	15.45714	0.112857
Machine 3	7	114.9	16.41429	0.261429
Machine 4	7	113	16.14286	0.309524
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	3.637143	3	1.212381	5.806157	0.003934	3.008787
Within Groups	5.011429	24	0.20881
Total	8.648571	27

P-value is 0.004 which is less than significance level 0.05, so we reject the null hypothesis.

3) At 5% level of significance we can conclude that the mean amount dispensed from the machines is not the same.

e) Here we have sampling bias.