Question

You will perform a Chi-Square test test. For the hypothesis test make sure to report the following steps:

1. Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.
2. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
3. Find the critical value(s) and identify the rejection region(s).
4. Find the appropriate standardized test statistic. If convenient, use technology.
5. Decide whether to reject or fail to reject the null hypothesis.
6. Interpret the decision in the context of the original claim.

A sports researcher is interested in determining if there is a relationship between the type of sport and type of team winning (home team versus visiting team). A random sample of 526 games is selected and the results are given below. Test the claim that the type of team winning is independent of the type of sport. Use α = 0.01.

	Football	Basketball	Soccer	Baseball
Home team wins	39	156	25	83
Visiting team wins	31	98	19	75

Answer 1

Null hypothesis- There is no significant relationship between type of sport and type of team winning.

Alternative hypothesis- There is significant relationship between type of sports and type of team winning.

Here the hypothesis is two tailed because of it is associated to an alternative hypotheses for which the sign of the potential difference is unknown. One more reason if we does not know whether the computed statistic will be at the right tail or at the left tail under the alternative hypothesis, the two tailed are considered.

From the table of chi square test the critical value for degree of freedom 3 at 0.01 level of significance is 11.345.

The test statistic is a chi-square random variable (Χ^2) defined by the following equation.

Χ^2 = Σ [ (Or,c - Er,c)2 / Er,c ] …................ (1)

Using equation (1) we find the test statistic = 3.2904

And the p-value is 0.348976

Since the p-value is 0.348976 is greater than the 0.01 level of significance it means this gives the weak evidence against the null hypothesis since we did not reject the null hypothesis.

Since we conclude that there is no significant relationship between type of sports and type of team winning.