Question

Investigate whether or not %Change is dependent on Location. You have the following cross-tabulations for the sample of 150 stores: Country 1 Frequency Count: - %Change - 1.0 to < 3.0 3.0 to < 4.0 4.0 to < 5.0 5.0 to 7.0 Total - Location (C) - Mall 11 11 32 7 61 Strip 3 26 20 11 19 7 38 Total 15 48 71 16 150 2 51 Location (C)- Country Total Percent of Columns: - %Change - 1.0 to < 3.0 3.0 to < 4.0 4.0 to < 5.0 5.0 to 7.0 Total Mall 18.0% 18.0% 52.5% 11.5% Strip 5.9% 51.0% 39.2% 3.9% 100.0% 10.0% 32.0% 47.3% 10.7% 100.0% 100.0% 100.0%

1. (a) Complete the four (4) missing boxes in the cross-tabulation table above.

2. (b) If you were to choose one store at random from the 150 in the group:

   1. (i) What is the probability it would be a Mall store with a %Change of less than 3?

   2. (ii) What is the probability the %Change would be 5% or more?

   3. (iii) What is the probability it would be store with a %Change in the range “4.0 to < 5.0” or a Strip store?

   4. (iv) What is the probability it would have a %Change in the range “4.0 to < 5.0” if you knew it was a Strip store?

3. Are “%Change” and “Location” independent or dependent?

   (i) What do we mean by “independent” and “dependent"? Explain in the context of this problem, including why it would be useful to know one way or the other.

   (ii) Use the tables above to explain whether or not you think the two variables are independent. Provide useful results to illustrate your conclusion.

Answer 1

Answer a:

Originally, we are given the following question-table:

Total Frequency Count % Change 1.0 to <3.0 3.0 to <4.0 4.0 to < 5.0 5.0 to 7.0 Total Location (c) Mail 11 Country 1 11 Strip 3 26 15 48 11 19 20 71 32 7 7 2 16 38 61 51 150

We can find the missing values as mentioned in the below table:

Frequency Count % Change 1.0 to <3.0 3.0 to <4.0 4.0 to < 5.0 5.0 to 7.0 Total Country 2.6% 28.9% 50.0% 18.4% 100% Location (c) Mail 18.0% 18.0% 52.5% 11.5% Total Strip 5.9% 10.0% 51.0% 32.0% 39.2% 47.3% 3.9% 10.7% 100% 100% 100%

Where Missing Value in a particular Cell of Column 'Country' = Cell value of column 'Country' from the original table / Total of 'Country' column

Answer i:

The probability that the selected location would be a Mall store with a %Change of less than 3 =

= Intersection cell value between row 1.0 to < 3.0 and a column 'mall' / 150

= 11 / 150

= 0.0733 or 7.33 %

Answer ii:

The probability that the chosen location has a % change of 5% or more =

= Total of row '5.0 to 7.0' / 150

= 16 / 150

= 0.1067 or 10.67 %

Answer iii:

The probability that the chosen store would be a store with a %Change in the range “4.0 to < 5.0” or a Strip store =

= ( Total of row '4.0 to < 5.0 + Total of column 'strip' ) / 150

= (71 + 51) / 150

= 122 / 150

= 0.4467 or 81.33 %

Answer iv:

The probability that the chosen location would have a %Change in the range “4.0 to < 5.0” if you knew it was a Strip store =

= Intersection cell value between the row '4.0 to <5.0' and column 'strip' / Total of column 'strip'

= 20 / 51

= 0.3922 or 39.22 %