WebAssign for Rosner's Fundamentals of Biostatistics, 8th Edition [Instant Access], Single-Term
WebAssign for Rosner's Fundamentals of Biostatistics, 8th Edition [Instant Access], Single-Term
8th Edition
ISBN: 9780357452905
Author: Rosner
Publisher: Cengage Learning US
bartleby

Videos

Textbook Question
Book Icon
Chapter 10, Problem 1P

Consider the Physicians’ Health Study data presented in Example 10.37 (p. 411).

How many participants need to be enrolled in each group to have a 90% chance of detecting a significant difference using a two-sided test with α = .05 if compliance is perfect?

Expert Solution & Answer
Check Mark
To determine

Find the number of participants need to be enrolled in each group to have a 90% chance of detecting a significant difference using a two-sided test with α = 0.05 and compliance is perfect.

Answer to Problem 1P

The number of participants need to enrol in each group to achieve 90% power is 18,469.

Explanation of Solution

From Example 10.37, it is known that p1=0.020,p2=0.025.

Where,

    p¯=p1+p22=0.020+0.0252=0.0225q¯=1p¯=10.0225=0.9775Δ=p1p2=0.0200.025=0.005   

From the given information, it is known that α=0.05,β=0.9.

Step-by-step procedure to obtain critical value using Excel:

  • In an empty cell of an Excel sheet, type “=NORMSINV(1-(0.05/2))”.
  • Click Enter.

The output obtained is as follows:

WebAssign for Rosner's Fundamentals of Biostatistics, 8th Edition [Instant Access], Single-Term, Chapter 10, Problem 1P , additional homework tip  1

Thus, z1α2=1.96.

Similarly, the value of z for 90% confidence level is obtained below:

WebAssign for Rosner's Fundamentals of Biostatistics, 8th Edition [Instant Access], Single-Term, Chapter 10, Problem 1P , additional homework tip  2

It can be written às follows:

z1β=z0.9=1.28

Using Equation 10.13, the sample size is computed as follows

n=2p¯q¯z1α/2+p1q1+p2q2z1β2Δ2n=2(0.0225)(0.9775)1.96+0.020(0.980)+0.025(0.975)1.282(0.05)2n=18468.5n18,469

Thus, the number of participants need to enrol in each group to achieve 90% power is 18469.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Find the critical value for a left-tailed test using the F distribution with a 0.025, degrees of freedom in the numerator=12, and degrees of freedom in the denominator = 50. A portion of the table of critical values of the F-distribution is provided. Click the icon to view the partial table of critical values of the F-distribution. What is the critical value? (Round to two decimal places as needed.)
A retail store manager claims that the average daily sales of the store are $1,500. You aim to test whether the actual average daily sales differ significantly from this claimed value. You can provide your answer by inserting a text box and the answer must include: Null hypothesis, Alternative hypothesis, Show answer (output table/summary table), and Conclusion based on the P value. Showing the calculation is a must. If calculation is missing,so please provide a step by step on the answers Numerical answers in the yellow cells
Show all work

Chapter 10 Solutions

WebAssign for Rosner's Fundamentals of Biostatistics, 8th Edition [Instant Access], Single-Term

Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License