/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 Interpreting Power Chantix (vare... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 33

Interpreting Power Chantix (varenicline) tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than \(8 \%\) of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a \(0.05\) significance level. Using \(0.18\) as an alternative value of \(p\), the power of the test is \(0.96\). Interpret this value of the power of the test.

Short Answer

Expert verified
The power of 0.96 means there is a 96% chance of detecting that more than 8% of users experience pain if the true proportion is 18%.

Step by step solution

01

- Understanding Hypothesis Testing

The power of a test refers to the probability that the test will correctly reject a false null hypothesis. This means the test will identify an effect when there is one.
02

- Define the Hypotheses

Set up the null hypothesis (H_0) and the alternative hypothesis (H_a):H_0: p = 0.08H_a: p > 0.08where p is the true proportion of Chantix users experiencing abdominal pain.
03

- Analyze the Power

The power of a test (0.96 in this case) shows how likely it is to reject the null hypothesis if the alternative hypothesis is true. Specifically, it tells us that there is a 96% chance of detecting an effect (i.e., abdominal pain rate higher than 8%) if the actual proportion of users experiencing abdominal pain is 18%.
04

- Contextual Interpretation

Since the power is 0.96, it means that the hypothesis test is very effective in detecting that more than 8% of Chantix users experience abdominal pain when the actual proportion is 18%.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hypothesis Testing
Hypothesis testing is a statistical method used to make inferences about a population parameter. We start with an initial assumption or claim about the population - this is known as the hypothesis. In scientific research, hypothesis testing serves as a tool to decide whether to accept or reject this initial claim. There are two main steps:
  • Formulating the null and alternative hypotheses.
  • Using a sample data to determine whether the null hypothesis should be rejected.
A well-conducted hypothesis test provides a systematic way to test predictions and make sound conclusions based on data.
Null Hypothesis
The null hypothesis, denoted as \( H_0 \), is a statement of no effect or no difference. It's the hypothesis that researchers typically try to disprove or nullify in hypothesis testing.
In our example, the null hypothesis is \( H_0: p = 0.08 \), which means that 8% of Chantix users experience abdominal pain. This represents the status quo or the common assumption that needs evidence to be challenged. The goal of the hypothesis test is to see if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
Alternative Hypothesis
The alternative hypothesis, denoted as \( H_a \) or \( H_1 \), is a statement that indicates the presence of a particular effect or difference. It's what researchers aim to support with evidence gathered from the sample data.
For the Chantix example, the alternative hypothesis is \( H_a: p > 0.08 \). This hypothesis asserts that more than 8% of Chantix users experience abdominal pain. If the sample data provides sufficient evidence, the null hypothesis will be rejected in favor of the alternative hypothesis.
  • The alternative hypothesis represents the change or effect the researchers are testing for.
  • It is directly opposed to the null hypothesis.
Significance Level
The significance level, denoted as \( \alpha \), is the probability of rejecting the null hypothesis when it is actually true. It's a threshold set by the researcher to decide how much risk they are willing to take of making a Type I error (false positive).
In our Chantix example, the significance level is set to \( 0.05 \). This means there is a 5% risk of concluding that more than 8% of users experience abdominal pain when, in fact, the actual proportion is 8% or less.
  • The choice of significance level impacts the decision-making process in hypothesis testing.
  • Common significance levels are 0.05, 0.01, and 0.10.
Statistical Power
Statistical power is the probability that a test will correctly reject a false null hypothesis. In simpler terms, it measures how likely the test is to detect an effect if there really is one.
For the case of Chantix, the power of the test is 0.96, meaning there is a 96% chance of detecting an abdominal pain rate higher than 8% if the actual rate is 18%.
  • High power is desirable because it means there is a lower probability of making a Type II error (false negative).
  • Factors influencing power include the sample size, significance level, and the true effect size.
To summarize, a high power value indicates that the hypothesis test is effective in detecting significant differences or effects when they truly exist.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Touch Therapy When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 280 trials, the touch therapists were correct 123 times (based on data in "A Close Look at Therapeutic Touch," Journal of the American Medical Association, Vol. 279, No. 13 ). Use a \(0.10\) significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective?

Store Checkout-Scanner Accuracy In a study of store checkout-scanners, 1234 items were checked for pricing accuracy; 20 checked items were found to be overcharges, and 1214 checked items were not overcharges (based on data from "UPC Scanner Pricing Systems: Are They Accurate?" by Goodstein, Journal of Marketing, Vol. 58). Use a \(0.05\) significance level to test the claim that with scanners, \(1 \%\) of sales are overcharges. (Before scanners were used, the overcharge rate was estimated to be about \(1 \% .)\) Based on these results, do scanners appear to help consumers avoid overcharges?

Tennis Instant Replay The Hawk-Eye electronic system is used in tennis for displaying an instant replay that shows whether a ball is in bounds or out of bounds so players can challenge calls made by referees. In a recent U.S. Open, singles players made 879 challenges and 231 of them were successful, with the call overturned. Use a \(0.01\) significance level to test the claim that fewer than \(1 / 3\) of the challenges are successful. What do the results suggest about the ability of players to see calls better than referees?

Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be \(0.1\). a. Use the critical value method with a \(0.05\) significance level to test the claim that the proportion of zeros equals \(0.1\). b. Use the \(P\) -value method with a \(0.05\) significance level to test the claim that the proportion of zeros equals \(0.1\). c. Use the sample data to construct a \(95 \%\) confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals \(0.1 ?\) d. Compare the results from the critical value method, the \(P\) -value method, and the confidence interval method. Do they all lead to the same conclusion?

Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Use a \(0.01\) significance level to test Mendel's claim that under the same circumstances, \(25 \%\) of offspring peas will be yellow. What can we conclude about Mendel's claim?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.