We appreciate your visit to Preparing to Check the Large Counts Condition for a Proportion z Test A doctor claims that runners tend to be optimistic but are they more. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To address the question, we need to prepare to check the large counts condition for a proportion z-test. This involves identifying the values for successes and failures in the samples of runners and walkers.
In the problem, we have:
1. Number of Runners Surveyed:
- Total runners surveyed: [tex]\( n_R = 80 \)[/tex]
2. Number of Walkers Surveyed:
- Total walkers surveyed: [tex]\( n_W = 100 \)[/tex]
3. Number of Optimistic Runners:
- Runners who scored as "optimistic": [tex]\( 68 \)[/tex]
4. Number of Optimistic Walkers:
- Walkers who scored as "optimistic": [tex]\( 72 \)[/tex]
To check the large counts condition, you need the expected number of successes and failures for both groups.
- For Runners:
- Expected number of successes: The number of optimistic runners, which is [tex]\( 68 \)[/tex].
- Expected number of failures: Total runners minus optimistic runners: [tex]\( n_R - \)[/tex] optimistic runners [tex]\( = 80 - 68 = 12 \)[/tex].
- For Walkers:
- Expected number of successes: The number of optimistic walkers, which is [tex]\( 72 \)[/tex].
- Expected number of failures: Total walkers minus optimistic walkers: [tex]\( n_W - \)[/tex] optimistic walkers [tex]\( = 100 - 72 = 28 \)[/tex].
Therefore, for your calculation, you have:
- Runners: [tex]\( n_R = 80 \)[/tex], 68 successes, and 12 failures.
- Walkers: [tex]\( n_W = 100 \)[/tex], 72 successes, and 28 failures.
These values will help determine if the sample sizes are sufficiently large to use a z-test for comparing proportions.
In the problem, we have:
1. Number of Runners Surveyed:
- Total runners surveyed: [tex]\( n_R = 80 \)[/tex]
2. Number of Walkers Surveyed:
- Total walkers surveyed: [tex]\( n_W = 100 \)[/tex]
3. Number of Optimistic Runners:
- Runners who scored as "optimistic": [tex]\( 68 \)[/tex]
4. Number of Optimistic Walkers:
- Walkers who scored as "optimistic": [tex]\( 72 \)[/tex]
To check the large counts condition, you need the expected number of successes and failures for both groups.
- For Runners:
- Expected number of successes: The number of optimistic runners, which is [tex]\( 68 \)[/tex].
- Expected number of failures: Total runners minus optimistic runners: [tex]\( n_R - \)[/tex] optimistic runners [tex]\( = 80 - 68 = 12 \)[/tex].
- For Walkers:
- Expected number of successes: The number of optimistic walkers, which is [tex]\( 72 \)[/tex].
- Expected number of failures: Total walkers minus optimistic walkers: [tex]\( n_W - \)[/tex] optimistic walkers [tex]\( = 100 - 72 = 28 \)[/tex].
Therefore, for your calculation, you have:
- Runners: [tex]\( n_R = 80 \)[/tex], 68 successes, and 12 failures.
- Walkers: [tex]\( n_W = 100 \)[/tex], 72 successes, and 28 failures.
These values will help determine if the sample sizes are sufficiently large to use a z-test for comparing proportions.
Thanks for taking the time to read Preparing to Check the Large Counts Condition for a Proportion z Test A doctor claims that runners tend to be optimistic but are they more. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
