Asked by zhamiya moore on Jun 08, 2024
Verified
Assuming that all necessary conditions are met, what needs to be changed in the formula 
, so that we can use it to construct a confidence interval estimate for the population proportion p?
A) The p̂ should be replaced by p.
B) The ta should be replaced by za.
C) The ta should be replaced by ta/2.
D) The ta should be replaced by za/2.
E) The p̂ should be replaced by za/2.
Confidence Interval
A range of values, derived from sample statistics, that is likely to contain the true value of an unknown population parameter with a specified level of confidence.
Population Proportion
A fraction or percentage that represents part of a whole or group within a population that shares a particular characteristic.
Formula
A symbolic representation of a principle or a set of mathematical relations, often used to solve problems or to define scientific laws.
- Comprehend the prerequisites for applying z-tests in hypothesis testing and the estimation of confidence intervals.
Verified Answer
JV
Ja'Quan VarnerJun 10, 2024
Final Answer :
D
Explanation :
To construct a confidence interval estimate for the population proportion p, we need to use the formula:
p̂ ± ta √((p̂(1-p̂))/n)
However, since the sample size is large (assuming all necessary conditions are met), we can use the normal distribution instead of the t-distribution. This means we need to replace ta with za/2, which gives us:
p̂ ± za/2 √((p̂(1-p̂))/n)
Therefore, the correct choice is D, which suggests replacing ta with za/2.
p̂ ± ta √((p̂(1-p̂))/n)
However, since the sample size is large (assuming all necessary conditions are met), we can use the normal distribution instead of the t-distribution. This means we need to replace ta with za/2, which gives us:
p̂ ± za/2 √((p̂(1-p̂))/n)
Therefore, the correct choice is D, which suggests replacing ta with za/2.
Learning Objectives
- Comprehend the prerequisites for applying z-tests in hypothesis testing and the estimation of confidence intervals.