The General Social Survey regularly asks individuals to disclose their religious affiliation. The following data represent the religious affiliation of young adults, aged 18 to 29, in the 1970s, 1980s, 1990s, and 2000s. Do the data suggest different proportions of 18- to 29-year-olds have been affiliated with religion in the past four decades? Use the α = 0.05 level of significance.
Table of contents
- 1. Intro to Stats and Collecting Data1h 14m
- 2. Describing Data with Tables and Graphs1h 56m
- 3. Describing Data Numerically2h 5m
- 4. Probability2h 17m
- 5. Binomial Distribution & Discrete Random Variables3h 6m
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- 7. Sampling Distributions & Confidence Intervals: Mean3h 23m
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - ExcelBonus23m
- Introduction to Confidence Intervals15m
- Confidence Intervals for Population Mean1h 18m
- Determining the Minimum Sample Size Required12m
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- 8. Sampling Distributions & Confidence Intervals: Proportion2h 10m
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10. Hypothesis Testing for Two Samples
Two Proportions
Problem 11.1.36b
Textbook Question
"Putting It Together: Salk Vaccine On April 12, 1955, Dr. Jonas Salk released the results of clinical trials for his vaccine to prevent polio. In these clinical trials, 400,000 children were randomly divided in two groups. The subjects in group 1 (the experimental group) were given the vaccine, while the subjects in group 2 (the control group) were given a placebo. Of the 200,000 children in the experimental group, 33 developed polio. Of the 200,000 children in the control group, 115 developed polio.What type of experimental design is this?
b. What are the treatments?"
Verified step by step guidance1
Step 1: Identify the type of experimental design by examining how the subjects were assigned and treated. Since 400,000 children were randomly divided into two groups, with one group receiving the vaccine and the other receiving a placebo, this is a randomized controlled experiment.
Step 2: Understand that a randomized controlled experiment involves randomly assigning subjects to different groups to compare the effects of treatments while controlling for confounding variables.
Step 3: Define the treatments in this experiment. Treatments refer to the specific conditions or interventions applied to each group. Here, the two treatments are the vaccine and the placebo.
Step 4: Clarify that the experimental group received the vaccine, which is the active treatment intended to prevent polio, while the control group received the placebo, which is an inactive substance used to compare against the vaccine's effect.
Step 5: Summarize that the experimental design is a randomized controlled trial, and the treatments are the vaccine (experimental treatment) and the placebo (control treatment).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Randomized Controlled Trial (RCT)
An RCT is an experimental design where participants are randomly assigned to different groups to receive either the treatment or a control (such as a placebo). This randomization helps reduce bias and allows for a fair comparison of outcomes between groups, making it the gold standard for testing the effectiveness of interventions.
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Control Group and Placebo
The control group receives a placebo or no treatment, serving as a baseline to compare the effects of the experimental treatment. A placebo is an inactive substance designed to mimic the treatment without therapeutic effect, helping to isolate the true impact of the vaccine by accounting for psychological or other non-specific effects.
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Treatment in Experimental Design
The treatment refers to the specific intervention being tested—in this case, the Salk vaccine. It is the variable manipulated by researchers to observe its effect on the outcome, such as the incidence of polio, compared to the control group that does not receive the treatment.
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