Question

the platium gasaver national fuelsaver corporation naufactures the platinum gasaver, a device they claim "may increase gas mileage by 22%" in an advertisment published in the des moines register, the gas mileages with and without the device were presented for 15 "identical" 5- liter vehicles. the percent changes in gas mileage for the vehicles were calculated and are presented here:

48.3 46.9 43.8 44.6 40.2 38.5 34.6 33.7

28.7 28.7 24.8 10.8 10.4 6.9 -12.4

The 12.4% decrease is gas mileage is an outlier in this data set

                       

(a) find the mean x(with line over it) and the standard deviation s.

(b) find x(with line over it) and s for the 14 observations that remain when you ignore the outlier. How does the outlier affect the vaules of x(with libe of it) and s?

(c) what do you think the advertisement means when it calls these vehicles "identical"

BOOK: THE PRACTICE OF BUSINESS STATISTICS USING DATA FOR DECISONS

MOORE, McCABE, DUCKWORTH, ALWAN

SECOND EDITON

PAGE 46 1.61

Answer 1

a ) let's use excel for calculation

First enter the given dataset in the excel column.

Then click on Data >ata Analysis >>> Descriptive Statistics >>>OK

Then select the range of the dataset

Look the following image:

Then click on OK, so we get the following output:

from the above output, we get

= 28.566667

s = 17.5642

Let's find outliers.

If the value of the given dataset outside ( - 2*s ,    + 2*s ) this interval then we say that it is outliers.

( - 2*s ,    + 2*s ) = ( 28.566667 - 2*17.5642 , 28.566667 +2*17.5642) = ( -6.56173 , 63.69507)

Only one data value is outside this interval as -12.4

So that -12.4 is an outlier.

b) Let's find mean and standard deviation after deleting -12.4

Look the following output

Note that -12.4 is smallest value among the given values.

So that the mean obtained from the 14 values after removing smallest one is increases.

Also when we remove outlier then the variability in the dataset decrease.