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Answer:
As the <em>p</em>-value is too small the null hypothesis will be rejected concluding that there is a higher proportion of people supporting the home team.
Step-by-step explanation:
The hypothesis to determine which team spectators at a football game support is:
<em>H₀</em>: There are equal proportions of people supporting the home team and the visiting team, i.e. <em>p</em>₁ = <em>p</em>₂.
<em>Hₐ</em>: There is a higher proportion of people supporting the home team than the visiting team, i.e. <em>p</em>₁ > <em>p</em>₂.
A <em>z</em>-test for difference between proportions can be used to perform the test.
The test statistic is:
Th decision rule is:
If the <em>p</em>-value of the test is less than the significance level <em>α </em>then the null hypothesis will be rejected and vice-versa.
The commonly used significance levels are 0.01, 0.05 and 0.10.
The <em>p</em>-value of the test is computed as, <em>p</em> = 0.002.
The <em>p</em>-value of the test is less than all the significance level.
Thus, the null hypothesis will be rejected at any of the three significance level.
Conclusion:
As the <em>p</em>-value is too small the null hypothesis will be rejected concluding that there is a higher proportion of people supporting the home team.