UNLV Airfare and Inflation Data Analytics Questions

Open-Ended 1: 

Dr. Jiyoung Kwon collected data from the U.S. Department of Transportation Domestic

Airline Fares Consumer Report. She found the average fare paid in 1997 was $173.80 with a

standard deviation of $76.305. The average fare paid in 2000 was $188.00 with a standard

deviation of $76.842. The consumer price index in 1997 was 159.4 while the consumer price

index was 169.3 in 2000. This is an inflation rate of 6.21%. The average fares increased 8.2%

over this time period.

Dr. Kwon also paired the airfares across the two time periods by routes. There were 1,049

different routes in the data set. The average difference in fares for each pair is $14.27 with a

standard deviation of $33.736. Dr. Kwon is interested in testing the claim that the population

mean difference in rates paired by route was more than $10.78. If the mean difference was

more than $10.78, the researcher would have evidence that airfares have grown faster than

inflation.

(a) Write the formal null hypothesis, alternative hypothesis and specify a level of significance

to test the researcher’s claim of interest.

(b) Perform the statistical test. Clearly state your reasoning and your conclusion. Note:

Critical values from the student t’s distribution appear at the end of the exam book.

(c) Based on your analysis, does the researcher have evidence that airfares increased faster

than inflation? Explain how this statistical test provides this conclusion. If Dr. Kwon

was interested in testing the claim that the population mean difference in rates paired

by route was more than $13.035, what conclusion would we research regarding this

claim. This difference in fares would result from a 7.5% increase in fares.

(d) What is the relationship between the Power of the Test and the probability of a Type

II error? What is the key obstacle with our ability to calculate the Power of the Test

in this application?

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Open-Ended 2: (33%)

Refer to the section below titled Marketing Data. The data includes sales data from 3 different

campaigns (‘C’, ‘S’, and ‘N’). Each campaign has 20 observations. The 5 different stores

are a blocking factor. The average daily unit sales for campaign C was 8.5 with a standard

deviation of 5.06. The average daily unit sales for campaign S was 9.7 with a standard

deviation of 5.07. The average daily unit sales for campaign N was 4.80 with a standard

deviation of 2.35. The analyst is interested in testing the claim that the campaigns result in

different average daily unit sales.

(a) Write a 95% Confidence interval for the population mean for daily unit sales with

campaign ’N’. Note: critical values are available at the end of the exam booklet.

(b) Write a 95% Confidence interval for the population mean for daily unit sales with

campaign ’C’. Note: critical values are available at the end of the exam booklet.

(c) To test the analyst’s question of interest, which approach that we have used to date in

this class is must appropriate? State the null hypothesis, alternative hypothesis and

the level of significance for this test.

(d) Perform the statistical test (output from R is available in the section titled Marketing

Data below). Clearly state your reasoning and your conclusion.

7

Marketing Data

model1<-aov(sales~campaign,data=marketing_data)

summary(model1)

## Df Sum Sq Mean Sq F value Pr(>F)

## campaign 2 260.9 130.47 6.883 0.0021 **

## Residuals 57 1080.4 18.95

## —

## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1

model2<-aov(sales~campaign+block,data=marketing_data)

summary(model2)

## Df Sum Sq Mean Sq F value Pr(>F)

## campaign 2 260.9 130.47 6.918 0.00207 **

## block 1 24.3 24.30 1.289 0.26116

## Residuals 56 1056.1 18.86

## —

## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1

Critical Values

qt(p=1-0.05/2,df=1048)

## [1] 1.96223

qt(p=1-0.05,df=1048)

## [1] 1.646309

qt(p=1-0.05/2,df=19)

## [1] 2.093024

qt(p=1-0.05,df=19)

## [1] 1.729133