Question

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Answer 1

Solution:-

(A) Test of independence.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: There is no difference between football fans and basketball fans on their likelihood of being superstitious.

Alternative hypothesis: There is difference between football fans and basketball fans on their likelihood of being superstitious. .

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for homogeneity.

Analyze sample data. Applying the chi-square test for homogeneity to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (2 - 1)
D.F = 1
E_r,c = (n_r * n_c) / n

Football - superstitious Basketball - superstitious Football - Not superstitious Basketball - Not- superstitious (O-E) 2/E 0.211 0.211 0.190 0.190

Fotball Superstitious Not superstitious Total Expected [Orc-Ecc)2/ E. Basketball 19 0.210526315789 210.190476190474 40 0.401002506265 Expected forc-Ecc)2/ E Total 19 0.210526315789 21 0.190476190474 400.401002506269 801


x= (Or,c - Erc) Erc

Χ² = 0.80

Χ²_Critical = 3.838

where DF is the degrees of freedom, r is the number of populations, c is the number of levels of the categorical variable, n_r is the number of observations from population r, n_c is the number of observations from level c of the categorical variable, n is the number of observations in the sample, E_r,c is the expected frequency count in population r for level c, and O_r,c is the observed frequency count in population r for level c.

The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 0.80.

We use the Chi-Square Distribution Calculator to find P(Χ² > 0.80) = 0.371.

Interpret results. Since the P-value (0.371) is greater than the significance level (0.05), we failed to reject the null hypothesis.

(A) Retain the null hypothesis, that there is no difference between football fans and basketball fans on their likelihood of being superstitious.