Question

In Exercises 1–10, based on the nature of the given data, do the following:

a. Pose a key question that is relevant to the given data.
b. Identify a procedure or tool from this chapter or the preceding chapters to address the key question from part (a).
c. Analyze the data and state a conclusion.

Video Games In a survey of subjects aged 18–29, subjects were asked if they play video games often or sometimes. Among 1017 males, 72% answered “yes.” Among 984 females, 49% answered “yes” (based on data from a Pew Research Center survey).

Accepted Answer

Step 1: Pose a key question relevant to the data. For example, 'Is there a significant difference in the proportion of males and females aged 18–29 who play video games often or sometimes?' Step 2: Identify the appropriate statistical procedure to address the key question. In this case, a hypothesis test for the difference between two population proportions (e.g., a two-proportion z-test) is suitable. Step 3: Define the null and alternative hypotheses. The null hypothesis (H₀) is that the proportions of males and females who play video games are equal (p₁ = p₂). The alternative hypothesis (H₁) is that the proportions are not equal (p₁ ≠ p₂). Step 4: Calculate the test statistic using the formula for the z-test for two proportions: z=(p_{1}-p_{2})(p_{c})(1-p_{c})(1n_{1}+1n_{2}), where p₁ and p₂ are the sample proportions, n₁ and n₂ are the sample sizes, and pₐ is the pooled proportion. Step 5: Compare the calculated z-value to the critical z-value (or use the p-value approach) at the chosen significance level (e.g., α = 0.05). Based on this comparison, decide whether to reject or fail to reject the null hypothesis and state the conclusion in the context of the problem.

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Key Concepts

Descriptive Statistics

Hypothesis Testing

Data Analysis Techniques