Question

In: Statistics and Probability

Reading Nook Bookstore has 750 retail outlets across the country. The sales director wanted to see...

Reading Nook Bookstore has 750 retail outlets across the country. The sales director wanted to see if Christmas music affects book sales in December. She randomly assigned some of the outlets to pipe in music and others not to. Then sales records for the month of December were kept. The results are shown in below. is there convincing evidence that there is an association between sales and christmas music?

<10,000 10-20,0000 >20,000

with music 5 18 7

without music 10 7 3

Type of test

Ho

Ha

Requirements

test statistic

Pvalue

Reject/fail to reject

Solutions

Expert Solution

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H0: there is no association between sales and Christmas music.

Alternative hypothesis: Ha: there is an association between sales and Christmas music.

We assume/given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 2

Number of columns = c = 3

Degrees of freedom = df = (r – 1)*(c – 1) = 1*2 = 2

α = 0.05

Critical value = 5.991465

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies

Column variable

Row variable

<10

10 to 20

>20

Total

With music

5

18

7

30

Without music

10

7

3

20

Total

15

25

10

50

Expected Frequencies

Column variable

Row variable

<10

10 to 20

>20

Total

With music

9

15

6

30

Without music

6

10

4

20

Total

15

25

10

50

Calculations

(O - E)

-4

3

1

4

-3

-1

(O - E)^2/E

1.777778

0.6

0.166667

2.666667

0.9

0.25

Test Statistic = Chi square = ∑[(O – E)^2/E] = 6.361111

χ2 statistic = 6.361111

P-value = 0.041563

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is an association between sales and Christmas music.


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