Question

] A marketing research firm wants to investigate the relationship between chip consumption and whether a person likes to watch professional football on television. One hundred randomly selected people are asked whether they eat chips and whether they watch football on television. The following results are obtained:

	Watches football	Does not watch football	Totals
Eats chips	20	45	65
Does not eat chips	5	30	35
Totals	25	75	100

1) State the null and alternative hypotheses [1 mark]:

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2) Calculate the test statistic. Please show how you calculate each expected cell total, show how you plug in to the appropriate equation for the test statistic, and show your final answer rounded to 4 decimal places. [6 marks]

3) The critical value for this test is 3.84146.

4) Based on this critical value, do you reject the null hypothesis? Please answer yes or no. [1 mark]



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5) In one sentence, conclude in the context of the original question [1 mark]

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6) Based on the result of your hypothesis test, do you think it is a good idea to advertise chips during football games, assuming ratings are high enough? Please answer yes or no. [1 mark]

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Answer 1

Answer 1:

The null and alternative hypotheses are:

H0: There is no association between eating chips and watching football (or Eating chips and watching football are independent)

Ha: There is association between eating chips and watching football (or Eating chips and watching football are dependent)

Answer 2:

Expected count in 4 decimal places are:

The Chi-Squared statistic is computed as follows:

χ² = 0.8654+0.2885+1.6071+0.5357

χ² = 3.2967

The test statistic is 3.2967

Answer 4:

Since it is observed that χ² = 3.2967 ≤ χ_c²​ = 3.84146, we don not reject null hypothesis.

Answer 5:

There is enough evidence to claim that the eating chips and watching football are dependent.

Answer 6:

No, it is not good idea to advertise chips during football game as based on hypothesis test we don't find any association between eating chips and watching football games.