9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

4:00 minutes

Problem 9.CR.2

Textbook 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 984 females, 49% answered “yes” (based on data from a Pew Research Center survey).

Verified step by step guidance

Step 1: Pose a key question relevant to the given data. For example, 'Is there evidence to suggest that the proportion of females aged 18–29 who play video games often or sometimes is significantly different from 50%?' This question focuses on testing whether the observed proportion (49%) differs from a hypothesized proportion (50%).

Step 2: Identify the appropriate statistical procedure or tool to address the key question. Since the problem involves proportions, a hypothesis test for a population proportion (such as a one-sample z-test for proportions) is suitable. This test will help determine if the observed proportion is significantly different from the hypothesized proportion.

Step 3: Set up the null and alternative hypotheses. The null hypothesis (H₀) is that the population proportion of females aged 18–29 who play video games often or sometimes is equal to 50% (p = 0.50). The alternative hypothesis (H₁) is that the population proportion is not equal to 50% (p ≠ 0.50).

Step 4: Calculate the test statistic using the formula for a z-test for proportions:

z = (p - p

₀)p₀(1-p₀)n, where p is the sample proportion (0.49), p₀ is the hypothesized proportion (0.50), and n is the sample size (984).

Step 5: Compare the calculated z-value to the critical z-value for the chosen significance level (e.g., α = 0.05). If the absolute value of the calculated z-value exceeds the critical z-value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Based on this comparison, state a conclusion about whether the proportion of females aged 18–29 who play video games often or sometimes is significantly different from 50%.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Survey Methodology

Survey methodology involves the techniques and processes used to collect data from respondents. In this context, understanding how the survey was conducted, including sample size and demographic targeting, is crucial for interpreting the results accurately. It helps in assessing the reliability and validity of the findings, such as the percentage of females who play video games.

Statistical Analysis

Statistical analysis refers to the methods used to summarize, interpret, and draw conclusions from data. In this case, analyzing the 49% of females who play video games involves calculating proportions and possibly comparing them to other demographics. This analysis can reveal trends and inform decisions based on the data collected.

Conclusion Drawing

Conclusion drawing is the process of interpreting the results of data analysis to make informed statements or decisions. After analyzing the survey data, one must synthesize the findings to answer the key question posed. This step is essential for translating statistical results into actionable insights, such as understanding gaming habits among young females.

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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.

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Textbook 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.

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