Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [confidence-interval]

In statistics, a confidence interval (CI) is a type of interval estimate (of a population parameter) that is computed from the observed data.

The confidence level is the frequency (i.e., the proportion) of possible confidence intervals that contain the true value of their corresponding parameter. In other words, if confidence intervals are constructed using a given confidence level in an infinite number of independent experiments, the proportion of those intervals that contain the true value of the parameter will match the confidence level.

789 questions
0
votes
1 answer

Clarification regarding length of confidence intervall

I'm having trouble with a problem, where I can't understand how my textbook's answer makes sense: An architect is measuring the distance between two points. Each value can be seen as an observation of a normal-distributed variable, with $\mu$ as…
PopeP
  • 1
0
votes
1 answer

Find the required sample size for the investigator.

An investigator interested in estimating a population mean wants to be 95% certain that the length of the confidence interval does not exceed 4. Find the required sample size for his study if the population standard deviation is 14. My…
user848500
0
votes
0 answers

Accuracy vs. probability in confidence interval

I have a little doubt regarding the confidence intervals. I know that if I enlarge the sample size, then the amplitude of the interval will be smaller, therefore, the interval will be more precise, but I also think that, as a result of this, the…
ESCM
  • 3,161
0
votes
0 answers

Finding a Confidence Interval for a 2 player game

It's been a while since I have done statistics so I am a bit rusty. I'm playing a two person game which results in either a win or a loss. I want to find a 95% confidence interval for a given players win rate over 50 games, 500 games, and 5000…
tdammon
  • 101
0
votes
0 answers

Construct an approximate 0.95 confidence interval for alpha (Pareto distribution)

I tried doing it by using the hint from the final answer but my answer is not the same. I also tried to do it using the mean and variance of Pareto distribution but I also did not get the right answer. Here is my answer: Can someone point out what…
ibuntu
  • 145
0
votes
0 answers

Equitailed confidence intervals of one sample.

I am working on confidence intervals and would like to know if I did it correctly. Let $X$ be a random variable. Find the $100(1-\alpha)$% CI for the parameter $\theta$ when 1), $X$ is Exponential with mean $\theta$. 2), $X$ is…
hyg17
  • 5,117
  • 4
  • 38
  • 78
0
votes
1 answer

How is a corelation of function inputs to its outputs is called in math?

So I have a function $f$ and for a set of argument intervals I have a set of its result intervals? Example: say for $f(x)$ I have $f(2..6) = -1..2$ and $-inf..+inf$ for all others (ones I do not care about or do not have info). How calculation and…
DuckQueen
  • 169
0
votes
0 answers

Coverage probability for Wilson Score with Continuity Correction

From A. Agresti & B.Coull, “Approximate Is Better than ”Exact” for IntervalEstimation of Binomial Proportions”,The American Statistician, vol. 52,no2, pp. 119-126, 1998 The graphs show that the coverage probability for Wald and Wilson are below the…
The Puternerd
  • 131
  • 3
0
votes
1 answer

Bus company confidence interval

To ensure adequate customer service, a bus company wants to estimate the average number of passengers on a bus during morning rush hours. A number of bus passengers is a random variable with standard deviation of $9.2$. According to records, the…
Onno Weerts
  • 11
0
votes
0 answers

Should I use invNorm or invT in this word problem? How should I plug "more than 2 dollars" into the confidence interval?

I was given this word problem: The weekly earnings of students in one age group are normally distributed with a standard deviation of 88 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample…
Hillmas
  • 9
0
votes
0 answers

Finding a two-sided confidence interval

Let $X_1, \dotsc, X_n$ be i.i.d. $N(\mu,\sigma^2)$, where $\sigma^2$ is known, but $\mu$ is unknown. Construct a two sided 95% CI for $\mu$ based on $X_1, \dotsc, X_n$? I am unsure how to go about this problem when there is an unknown involved.
Topper Jmole
  • 1
0
votes
1 answer

Estimate the variance from the biggest and the smallest data

What is the estimation that we can use? The answer is n=183.
Ray Jasson
  • 425
0
votes
1 answer

Confidence interval - computing task

I'm planning to write a small app for a tedious task: Generating pdf based on a existing template (.txt basically) Binding specific data (some text, recipient, etc) to that template Suppose I have 100 pdf to generate. I expect $±100$% confidence…
roland
  • 137
0
votes
1 answer

Calculating this confidence Interval and making assumptions

Here is the question: A surveyor conducts research on 4148 households, randomly selected. An estimate of $7.9\%$ unemployment was obtained from a survey of $4148$ people. Construct a $95\%$ confidence interval with this data. Solution: An…
Twenty-six colours
  • 1,881
0
votes
1 answer

In order to take a confidence interval, why do we need the sampling distribution to be normal?

I'm reading a book right now on elementary statistics and I'm confused at this passage: The normal approximation is crucial to the precision of these confidence intervals. Section 4.4 provides a more detailed discussion about when the normal model…
Jwan622
  • 5,704
1
2
3