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for independent random samples

were selected one from each

fast food chain

for each observational unit

the drive through time was

recorded no quantitative

we ONLY used atechnique

for 2population Means

NEED to compare 3t

Packet 12: Analysis of Variance (ANOA) Textbook material: Supplemental Chapter 28

After completing this material, you should be able to:

• conduct an analysis of variance f-test with the appropriate StatCrunch output.

• determine when it is appropriate to consider multiple comparisons and interpret the results provided in

StatCrunch output.

• state when it is valid to use this procedure

Goal:

Example: For fast-food restaurants, the drive-through window is an increasing source of revenue. The chain that offers

the fastest service is likely to attract additional customers. Each month, QSR magazine publishes its results of drive-

through service times (from menu board to departure) at fast-food chains. In a recent month, the drive-through service

times of random sample of 20 customers from Burger King, McDonald’s, Wendy’s, and White Castle were recorded.

— What type of samples were selected? What variable was recorded? Why can none of the inferences we’ve discussed

so far be used to analyze this data?

— What hypotheses are we interested in testing?

Now we need a way to test these hypotheses. We cannot simply use a t-test because there is no way to “take the

difference” of more than two different means – it just doesn’t make sense. To get around this problem, we need to use a

different technique – we will use a new test statistic, called an F-statistic. The F-statistic is constructed from two different

variances (hence, analysis of variance) even though our goal is to compare several means.

When comparing two variances, we look at the ratio of those variances and use the F-distribution. So, the test statistic

that we’re interested in is the following:

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to compare 3T population Means

4independent random samples

drivethrough times

Hott BK.M HC.M W.tt _WC

Ha some difference inthemedns

fMStydstat Mst _treatment

Mse Crunch NSE error

labels

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spread between

MSE sample Means

Fuse spread within a

distribution

if null hypothesis is true

then the corresponding

sample Means should be very

SIMILAR results in a

small numerator in the

Fstatistic Alarge spread

in the numerator suggests

the hull hypothesis is likely

Not true