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 (way back in Section 1.5), name at least one type of bias that might be present in this research. Briefly explain.

Answer 1

Solution :

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.

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