Complete Question
The complete question is shown on the first uploaded image
Answer:
Using 2SD Method
The confidence interval is
The interval notation :
The interval notation and the sample proportion ± the margin of error
notation:
The interpretation
There is 95% confidence that the true proportion of those that dislike cilantro lie within the upper(0.212) and the lower(0.108) limit of the calculate confidence interval
Using theory-based method
The 95% confidence interval is
The interval notation :
The interval notation and the sample proportion ± the margin of error
notation:
The interpretation
There is 95% confidence that the true proportion of those that dislike cilantro lie within the upper(0.211) and the lower(0.109) limit of the calculate confidence interval
Using theory-based method
The 88% confidence interval is
The interval notation :
The interval notation and the sample proportion ± the margin of
error notation:
The interpretation is
There is 88% confidence that the true proportion of those that dislike cilantro lie within the upper(0.200 ) and the lower(0.120) limit of the calculate confidence interval.
Step-by-step explanation:
From the question we are told that
The number sample size is n = 200
The number of people that dislike cilantro is k = 32
Generally the sample proportion is mathematically represented as
=>
=>
Generally 2SD confidence interval is mathematically represented as
substituting value
=>
This can also be represented as
=>
Generally this confidence interval can be interpreted as
There is 95% confidence that the true proportion of those that dislike cilantro lie within the upper and the lower limit of the calculate confidence interval
Using theory-based method estimate 95% confidence interval
Generally from the question the confidence level is 95% hence the level of significance is calculated as
=>
The critical value of from the normal distribution table is
Generally the confidence level using theory base method is
=>
This can also be represented as
=>
Generally this confidence interval can be interpreted as
There is 95% confidence that the true proportion of those that dislike cilantro lie within the upper(0.211) and the lower(0.109) limit of the calculate confidence interval
Using theory-based method estimate 88% confidence interval
Generally from the question the confidence level is 95% hence the level of significance is calculated as
=>
The critical value of from the normal distribution table is
Generally the confidence level using theory base method is
=>
This can also be represented as
=>
Generally this confidence interval can be interpreted as
There is 88% confidence that the true proportion of those that dislike cilantro lie within the upper(0.200 ) and the lower(0.120) limit of the calculate confidence interval
