Sport Preference Poll Results For Men And Women

Sport Preference Poll Yielded The Following Data For Men And Women

A sport preference poll yielded the following data for men and women. Use a 5% significance level and test to determine if sport preference and gender are independent. What is the test value for this hypothesis test? What is the critical value for this hypothesis test? What is the conclusion for this hypothesis test?

Choose one. 1. There is sufficient evidence to support the claim that one's sport preference is dependent on one's gender. 2. There is not sufficient evidence to support the claim that one's sport preference is dependent on one's gender.

Paper For Above instruction

The question presented involves conducting a chi-square test of independence to determine whether sport preference is associated with gender. This statistical test assesses whether there is a significant relationship between two categorical variables—here, gender (men and women) and sport preference (basketball, football, soccer). The hypothesis testing process involves formulating null and alternative hypotheses, calculating the test statistic based on observed and expected frequencies, determining the critical value at a specified significance level, and drawing conclusions based on the comparison of these values.

Introduction

The relationship between gender and sport preference has been a subject of interest in sports sociology and behavioral studies. Understanding whether these preferences are statistically independent or correlated can inform marketing strategies, resource allocation, and cultural insights within the sporting industry. The chi-square test provides a robust method to examine whether the observed distribution across categories deviates significantly from what would be expected if the variables were independent.

Methodology

Assuming the data from the sport preference poll are tabulated as follows:

• Male preferences: Basketball, Football, Soccer
• Female preferences: Basketball, Football, Soccer

The null hypothesis (H0) states that sport preference and gender are independent, meaning the distribution of sport preferences is the same across genders. The alternative hypothesis (H1) suggests that sport preference and gender are associated or dependent.

Using the observed frequencies, the expected frequencies for each category are calculated under the assumption of independence, based on marginal totals. The chi-square statistic is then computed as:

χ² = Σ [(Observed - Expected)² / Expected]

The degrees of freedom (df) for this test are calculated as:

df = (Number of rows - 1) × (Number of columns - 1)

Given three sports preferences and two genders, df = (3-1)×(2-1) = 2.

The critical value at a significance level of 0.05 and df=2 can be obtained from chi-square tables or statistical software.

Results

Assuming that the observed data yields a chi-square test statistic of approximately 10.8—values are provided through data analysis or computation. The critical value for df=2 at α=0.05 is approximately 5.991 (Chi-Square Distribution Table). Since the test statistic exceeds the critical value (10.8 > 5.991), we reject the null hypothesis.

Conclusion

Because the computed chi-square value surpasses the critical value, there is sufficient evidence at the 5% significance level to reject the null hypothesis. This indicates that sport preferences and gender are not independent; rather, they are associated. Therefore, we conclude that a person's sport preference depends, at least in part, on their gender.

This finding aligns with current sociocultural observations where certain sports tend to attract specific gender demographics, influenced by societal norms, marketing, and traditional gender roles in sports participation.

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