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.
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- 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
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - Excel23m
- Introduction to Confidence Intervals15m
- Confidence Intervals for Population Mean1h 18m
- Determining the Minimum Sample Size Required12m
- Finding Probabilities and T Critical Values - Excel28m
- Confidence Intervals for Population Means - Excel25m
- 8. Sampling Distributions & Confidence Intervals: Proportion2h 10m
- 9. Hypothesis Testing for One Sample5h 8m
- Steps in Hypothesis Testing1h 6m
- Performing Hypothesis Tests: Means1h 4m
- Hypothesis Testing: Means - Excel42m
- Performing Hypothesis Tests: Proportions37m
- Hypothesis Testing: Proportions - Excel27m
- Performing Hypothesis Tests: Variance12m
- Critical Values and Rejection Regions28m
- Link Between Confidence Intervals and Hypothesis Testing12m
- Type I & Type II Errors16m
- 10. Hypothesis Testing for Two Samples5h 37m
- Two Proportions1h 13m
- Two Proportions Hypothesis Test - Excel28m
- Two Means - Unknown, Unequal Variance1h 3m
- Two Means - Unknown Variances Hypothesis Test - Excel12m
- Two Means - Unknown, Equal Variance15m
- Two Means - Unknown, Equal Variances Hypothesis Test - Excel9m
- Two Means - Known Variance12m
- Two Means - Sigma Known Hypothesis Test - Excel21m
- Two Means - Matched Pairs (Dependent Samples)42m
- Matched Pairs Hypothesis Test - Excel12m
- Two Variances and F Distribution29m
- Two Variances - Graphing Calculator16m
- 11. Correlation1h 24m
- 12. Regression3h 33m
- Linear Regression & Least Squares Method26m
- Residuals12m
- Coefficient of Determination12m
- Regression Line Equation and Coefficient of Determination - Excel8m
- Finding Residuals and Creating Residual Plots - Excel11m
- Inferences for Slope31m
- Enabling Data Analysis Toolpak1m
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- Prediction Intervals13m
- Prediction Intervals - Excel19m
- Multiple Regression - Excel29m
- Quadratic Regression15m
- Quadratic Regression - Excel10m
- 13. Chi-Square Tests & Goodness of Fit2h 21m
- 14. ANOVA2h 28m
9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
Problem 11.2.2
Textbook Question
Identifying Hypotheses Refer to the data given in Exercise 1 and assume that the requirements are all satisfied and we want to conduct a hypothesis test of independence using the methods of this section. Identify the null and alternative hypotheses.
Verified step by step guidance1
Step 1: Understand the context of the problem. A hypothesis test of independence is used to determine whether two categorical variables are independent or associated. Independence means that the occurrence of one variable does not affect the occurrence of the other.
Step 2: Define the null hypothesis (H₀). The null hypothesis in a test of independence states that the two variables are independent. In mathematical terms, this can be expressed as: , where A and B are the two categorical variables.
Step 3: Define the alternative hypothesis (H₁). The alternative hypothesis states that the two variables are not independent, meaning there is an association between them. In mathematical terms, this can be expressed as: .
Step 4: Ensure that the requirements for conducting the test are satisfied. These typically include having a sufficiently large sample size and ensuring that the expected frequencies in each cell of the contingency table are at least 5.
Step 5: Prepare to use the chi-square test statistic to evaluate the hypotheses. The test statistic is calculated using the formula: , where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Null Hypothesis
The null hypothesis (H0) is a statement that indicates no effect or no difference in the context of a statistical test. It serves as a default position that assumes any observed differences in data are due to random chance. In hypothesis testing, the goal is to gather evidence to either reject or fail to reject the null hypothesis based on sample data.
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Step 1: Write Hypotheses
Alternative Hypothesis
The alternative hypothesis (H1 or Ha) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. It represents the researcher's claim or the outcome they are trying to prove. In hypothesis testing, if the evidence is strong enough to reject the null hypothesis, the alternative hypothesis is considered supported.
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Step 1: Write Hypotheses
Hypothesis Test of Independence
A hypothesis test of independence is used to determine whether there is a significant association between two categorical variables. This test evaluates whether the distribution of one variable differs across the levels of another variable. Commonly, the Chi-square test is employed for this purpose, allowing researchers to assess the relationship between the variables based on observed and expected frequencies.
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Step 1: Write Hypotheses
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