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A survey of 450 randomly chosen U.S. adults found that 35% of the 200 men and 40% of the 250 women attended a college football game during the past month. Do these data provide statistical evidence at the [tex]\alpha = 0.01[/tex] level that men are more likely than women to attend football games?

Be sure to:

1. State the parameter.
2. Check conditions.
3. Perform calculations.
4. Make conclusions.

Answer :

Final answer:

A two-proportion z-test is performed to determine if men are more likely than women to attend football games. The calculations show that there is not enough evidence to support this claim at a significance level of 0.01.

Explanation:

To determine if there is statistical evidence that men are more likely than women to attend football games, we need to perform a hypothesis test. The parameter of interest is the difference in proportions between men and women who attended a football game. We will perform a two-proportion z-test to test the null hypothesis that the proportions are equal.

  1. Conditions: We assume the sample is random, and the sample sizes are large enough for the normal approximation to apply. The conditions are satisfied.
  2. Calculations: We calculate the test statistic z using the formula: z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2)), where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes. The test statistic is z = (0.35 - 0.40) / sqrt(0.375 * (1 - 0.375) * (1/200 + 1/250)) = -1.71
  3. Conclusion: The p-value associated with a test statistic of -1.71 is approximately 0.088. Since the p-value is greater than the significance level of 0.01, we do not have enough evidence to reject the null hypothesis. Therefore, we do not have statistical evidence to conclude that men are more likely than women to attend football games.

Learn more about Hypothesis testing here:

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