A marketing research rm examines the relationship between wine consumption and w

Question

A marketing research rm examines the relationship between wine consumption and whether a person likes to watch professional tennis on television. One hundred randomly selected people are asked whether they drink wine and whether they watch tennis. The following results are obtained:

Watch tennis

Do not watch tennis

Totals

Drink wine

16

24

40

Do not drink wine

4

56

60

Totals

20

80

100

1) What is the appropriate test for this problem (1 points)?

2) Set up the null and alternative hypotheses (2 points).

3) Write the formula of the test statistic (2 points).

4) Calculate the test statistic based on the formula (5 points).

5) Use Excel to calculate the p-value. Should we reject the null hypothesis at 5% significance level (5 points)?

6) Given the results of the test, does it make sense to advertise wine during a televised tennis match (assuming that the ratings for the tennis match are high enough)? Explain.

Watch tennis

Do not watch tennis

Totals

Drink wine

16

24

40

Do not drink wine

4

56

60

Totals

20

80

100

Explanation / Answer

1) Appropriate test - chi-square test of independence

2)

H0: Watching tennis and drinking wine are independent

H1: Watching tennis and drinking wine are not independent

3)

chi-square = summation (Oi - Ei)^2/Ei

4)

chi-square = 16.667

df = 1

5)

p-value = 0.000045 (=CHISQ.DIST.RT(16.667,1))

6)

As p-value is less than the significance level of 0.05, we reject null hypothesis

this means driking wine and watching tennis are not independent. It is advisable to advetise wine during a televised tennis match.

Observed Watch Tennis Do no watch tennis total Drink wine 16 24 40 Don’t Drink Wine 4 56 60 Total 20 80 100

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