Math Problem Statement
Use the sample data and confidence level given below to complete parts (a) through (d).
A drug is used to help prevent blood clots in certain patients. In clinical trials, among
44054405
patients treated with the drug,
185185
developed the adverse reaction of nausea. Construct a
9595%
confidence interval for the proportion of adverse reactions.
Question content area bottom
Part 1
a) Find the best point estimate of the population proportion p.
enter your response here
(Round to three decimal places as needed.)
Solution
To find the best point estimate of the population proportion , we use the formula:
where:
- is the number of patients who developed the adverse reaction (nausea),
- is the total number of patients treated.
From the problem:
- ,
- .
Now calculate :
Thus, the best point estimate of the population proportion is:
Would you like further details or explanations on this?
Here are 5 follow-up questions:
- How would you calculate the margin of error for a confidence interval?
- What formula is used to construct a confidence interval for a population proportion?
- How does increasing the confidence level affect the width of the confidence interval?
- Why is the point estimate of a population proportion important in statistics?
- What assumptions must be met for the confidence interval calculation to be valid?
Tip: Always check if the sample size is large enough to assume a normal distribution for proportions when constructing confidence intervals.
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Population Proportion
Formulas
Point estimate of population proportion: p̂ = x/n
Confidence interval for population proportion: p̂ ± Z * sqrt[(p̂(1-p̂))/n]
Theorems
Central Limit Theorem (for large sample size approximation)
Suitable Grade Level
Undergraduate/College level
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