QuestionA student was asked to find a confidence interval for the population proportion of students who take notes using data from a random sample of size . Which of the following is a correct interpretation of the interval ?
Check all that are correct.
There is a 98\% chance that the proportion of the population is between 0.1 and 0.31 .
The proportion of all students who take notes is between 0.1 and of the time.
With confidence, a randomly selected student takes notes in a proportion of their classes that is between 0.1 and 0.31 .
With confidence, the proportion of all students who take notes is between 0.1 and 0.31 .
There is a chance that the proportion of notetakers in a sample of 90 students will be between 0.1 and 0.31 .
Studdy Solution
STEP 1
What is this asking?
Which statements correctly describe what a 98% confidence interval from 0.1 to 0.31 *actually* means?
Watch out!
Confidence intervals are tricky!
Don't confuse the chances of a *single* sample with the confidence over *many* samples.
STEP 2
1. Understand Confidence Intervals
2. Analyze the Statements
STEP 3
Imagine taking tons of samples of 90 students and calculating a confidence interval from each sample.
A 98% confidence level means that about 98% of those intervals would *actually* contain the *true* proportion of *all* students who take notes.
It's about the long-run success rate of the *method*, not about a single interval!
STEP 4
"There is a 98% chance that the proportion of the population is between 0.1 and 0.31." This is wrong!
The true proportion is a fixed, but unknown, value.
It's either in the interval or it's not.
There's no probability involved for a single interval.
STEP 5
"The proportion of all students who take notes is between 0.1 and , 98% of the time." This is also incorrect.
The population proportion doesn't change over time (at least not in the context of this problem!). It's a constant value.
STEP 6
"With 98% confidence, a randomly selected student takes notes in a proportion of their classes that is between 0.1 and ." Nope, this isn't right either.
The confidence interval is about the *population* proportion, not about individual students.
STEP 7
"With 98% confidence, the proportion of *all* students who take notes is between 0.1 and ." Yes!
This is the correct interpretation.
It means we're 98% confident that our interval captures the true proportion of note-takers among *all* students.
STEP 8
"There is a 98% chance that the proportion of notetakers in a sample of 90 students will be between 0.1 and ." This is incorrect.
The confidence interval is about the *population* proportion, not the sample proportion.
We already *know* the sample proportion from our data; it's the *population* proportion we're trying to estimate.
STEP 9
The only correct statement is: With 98% confidence, the proportion of all students who take notes is between 0.1 and .
Was this helpful?
