Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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4:26 minutes

Problem 9.CR.3

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 1017 males, 72% answered “yes.” 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 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-p₂)(p_c)(1-p_c)(1n₁+1n₂), 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

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

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset. This includes measures such as mean, median, mode, and percentages, which help in understanding the distribution and trends within the data. In the context of the survey, calculating the percentage of males and females who play video games provides a clear overview of gaming habits among different genders.

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences or draw conclusions about a population based on sample data. It involves formulating a null hypothesis and an alternative hypothesis, then using statistical tests to determine if there is enough evidence to reject the null hypothesis. In this case, one might test whether there is a significant difference in gaming frequency between males and females.

Data Analysis Techniques

Data analysis techniques encompass various methods used to inspect, clean, and model data to discover useful information. Techniques such as chi-square tests for categorical data or t-tests for comparing means can be applied to analyze the survey results. These methods help in drawing conclusions about the gaming habits of different demographics based on the collected data.

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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.

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).

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.

IQ Scores of Twins Listed below are IQ scores of twins listed in Data Set 12 “IQ and Brain Size” in Appendix B. The data are pairs of IQ scores from ten different families.

Textbook Question

Smoking Cessation Programs Among 198 smokers who underwent a “sustained care” program, 51 were no longer smoking after six months. Among 199 smokers who underwent a “standard care” program, 30 were no longer smoking after six months (based on data from “Sustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,” by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). We want to use a 0.01 significance level to test the claim that the rate of success for smoking cessation is greater with the sustained care program. Test the claim using a hypothesis test.

Textbook Question

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Textbook Question

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In Exercises 9–12, use the randomization procedure for the indicated exercise.

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