We appreciate your visit to A sociologist claims that tex 25 tex of adults would describe themselves as organized A random sample of 100 adults reveals 42 who describe themselves. 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 determine if the conditions for inference are met, we need to check three main conditions: Random, 10% Condition, and Large Counts.
1. Random Condition:
We have a random sample of 100 adults. This means the sample was selected randomly from the population, which helps ensure that it is representative of the population.
2. 10% Condition:
To apply statistical inference, the sample size should be less than 10% of the entire population. Since we are dealing with 100 adults, we assume this is less than 10% of the total adult population. This assumption should hold because 100 is typically much smaller than the total number of adults in any large population setting.
3. Large Counts Condition:
For the normal approximation to be valid, both [tex]\( np_0 \)[/tex] and [tex]\( n(1-p_0) \)[/tex] must be at least 10, where [tex]\( n \)[/tex] is the sample size and [tex]\( p_0 \)[/tex] is the hypothesized population proportion (0.25 in this case).
- Calculate [tex]\( np_0 \)[/tex]:
[tex]\[
np_0 = 100 \times 0.25 = 25.0
\][/tex]
This is at least 10.
- Calculate [tex]\( n(1-p_0) \)[/tex]:
[tex]\[
n(1-p_0) = 100 \times (1 - 0.25) = 100 \times 0.75 = 75.0
\][/tex]
This is also at least 10.
Since both [tex]\( np_0 = 25.0 \)[/tex] and [tex]\( n(1-p_0) = 75.0 \)[/tex] are greater than 10, the Large Counts condition is satisfied.
Given these checks, all conditions for inference are met, indicating we can proceed with further statistical analysis to determine if there is convincing evidence that more than 25% of adults describe themselves as organized.
1. Random Condition:
We have a random sample of 100 adults. This means the sample was selected randomly from the population, which helps ensure that it is representative of the population.
2. 10% Condition:
To apply statistical inference, the sample size should be less than 10% of the entire population. Since we are dealing with 100 adults, we assume this is less than 10% of the total adult population. This assumption should hold because 100 is typically much smaller than the total number of adults in any large population setting.
3. Large Counts Condition:
For the normal approximation to be valid, both [tex]\( np_0 \)[/tex] and [tex]\( n(1-p_0) \)[/tex] must be at least 10, where [tex]\( n \)[/tex] is the sample size and [tex]\( p_0 \)[/tex] is the hypothesized population proportion (0.25 in this case).
- Calculate [tex]\( np_0 \)[/tex]:
[tex]\[
np_0 = 100 \times 0.25 = 25.0
\][/tex]
This is at least 10.
- Calculate [tex]\( n(1-p_0) \)[/tex]:
[tex]\[
n(1-p_0) = 100 \times (1 - 0.25) = 100 \times 0.75 = 75.0
\][/tex]
This is also at least 10.
Since both [tex]\( np_0 = 25.0 \)[/tex] and [tex]\( n(1-p_0) = 75.0 \)[/tex] are greater than 10, the Large Counts condition is satisfied.
Given these checks, all conditions for inference are met, indicating we can proceed with further statistical analysis to determine if there is convincing evidence that more than 25% of adults describe themselves as organized.
Thanks for taking the time to read A sociologist claims that tex 25 tex of adults would describe themselves as organized A random sample of 100 adults reveals 42 who describe themselves. 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
