Confidence interval Definition and 102 Threads

In experiment A: I observe an event 2 times in 2 trials. In experiment B: I observe an event 100 times in 100 trials. In both cases, I calculate a frequency of 100% In both cases, I calculate a 95% confidence interval of (1, 1). But intuitively the result of experiment B is "stronger" than...

I am refreshing on this... I think there is a mistake on the circled part in red...right? not correct symbol for sample mean...This is the part that i need clarity on. The other steps to solution are pretty easy to follow...as long as one knows the t-formula and also the knowledge to...

I think (e) is wrong because the proportion should be out of the whole population, not only in a certain class and option (a) to (d) looks like identical to me so I answered (a), (b), (c) and (d) but my answer is wrong. Where is my mistake? Thanks

Hey! 😊 For $n \in \mathbb{N}$ we consider the discrete statistical product model $(X, (\mathbb{P}_{\theta})_{\theta\in \Theta})$ with $X=\mathbb{N}^n$, $\Theta=\mathbb{N}$ and $p_{\theta}(x_i)=\frac{1}{\theta}1_{\{1\leq x_i\leq \theta\}}$ forall $x_i\in \mathbb{N}$, $\theta\in \Theta$. Let...

Hey! 😊 (a) In winter, the roads around Lake Macatawa are salted. To study the impact of this on Lake Macatawa, students took $32$ water samples from the western basin of the lake and Sodium content (in parts per million, ppm) determined. As a result, the students have receive the following...

Hey! :giggle: From two populations of small and medium enterprises, we collect two random and independent samples of size $n_1 = 64$ and $n_2 = 36$ enterprises respectively. If we calculate for the companies of the first sample average sales of $9$ thousand euros and a variation of $4$, while...

Here is the question I'm struggling with (Q1) : I just... I just don't understand what my first step is. Whats my barx1 and barx2? (bar x = mean, x1 = subscript 1) My thoughts on approaching this question : barX1 - barX2 `~ N(u1-u2, sd1^2/n1 + sd2^2/n2) Find Z value when p = 0.975, z = + or...

I read that confidence interval on standard deviation can be found using chi-square distribution. If I have a sample size N=500, and sample standard deviation= 3 with mean=0, and I need a 95% confidence, I wasn't sure what to set for degrees of freedom in chi-square formula. Is the degrees of...

I learned that the confidence interval and a two sided hypothesis test (test for difference) agree if both have the same significance level. Is that also true for one sided hypothesis tests? For instance, must a right-tailed Hypothesis test with alpha = 0.05 agree with the 95% confidence level...

I have experimental spectrum in which y-axis is intensity values, and x-axis is frequency values. Int - array of experimental intensities (y-axis). w - array of frequencies (x-axis). I know the view of theoretical function that must describe the obtained spectrum. I explicitly set the function...

I tried to derive an equation for one sample mean to converge to another sample mean within a 95% confidence interval, but I know I am wrong. Can someone tell me what I did wrong, and what is the correct formula? Suppose: ##\hat{x_1},\hat{\sigma_1},N## are a sample mean, standard deviation...

Hello. I am bewildered by so many different notions of probability distribution percentages, i.e. the proportion of values that lie within certain standard deviations from the mean. (1) There is a Chebyshev's inequality: - for any distribution with finite variance, the proportion of the...

Hello, I have been struggling with this question for a few days now would appreciate being walked through it! :) Data are collected on the wingspans of adult robins. For N=20 birds, the sample mean and variance are given by \overline{x}=9.5cm and s^{2}=2.6^{2}cm^{2} a) If we assume that the...

Hello. Math is not my strongest part, yet, so I will be very grateful for your help and for giving the answer in sort of "plain" English, meaning that it will be great if you don't go too deep into the rabbit hole using difficult terminology, as these distribution issues are truly difficult for...

A simple random sample of 400 high school football players was taken in order to estimate the mean weight of all high school football players. The sample has a mean of 198 lbs. and a standard deviation 26 lbs. Construct the 99% confidence interval estimate of the mean weight of all high school...

Hey! :o A research institute wants to establish a confidence interval for the quota of working people in a city. Let $\hat{p}_n $ be the estimated quota, based on a sample of size $n$. It is assumed that $n> 30$. How can one determine the length of the confidence interval? Generally this is...

Hey! :o The variable $X$ is normally distributed with unknown expected value $\mu$ and unknown variance $\sigma^2$. I want to determine the confidence interval for $\mu$ for $n=22; \ \overline{X}_n=7.2; \ S'=4; \ 1-\alpha=0.90$. Is $S'$ the standard deviation? (Wondering) In some notes...

Homework Statement The following two samples are corrosion values for 20 untreated pipes (Xi) and 20 surface treated pipes (Yi) ∑Xi = 950, ∑Xi2 = 46344 and ∑Yi = 1092, ∑Yi2 = 62136 We want to examine if there is basis to claim that the surface treatment reduce corrosion. a) 1: Find a 95%...

Confidence Interval or the lack of it... It is 1581 Anno Domini. At the Undergraduate School of UMUC, besides Assistant Academic Director of Mathematics and Statistics, I am also the Undergraduate School-appointed CPA, Coffee Pot Attendant. It is a very important office sponsored by the...

Homework Statement Hi, Alright so I have some confusion on when to use specific tests and the z vs t test. Given this example (not my homework) could someone please clarify. Alright say you have a random sample of size 200. You find the sample mean to be 10 and the sample standard deviation...

Homework Statement Both images are 2 consecutive pages of my notes . In this theory , i was told to use z-distribution when the sample size is large ( more than 30) and the standard deviation of the population , σ is known) . However , in the 2nd image , i was told to replace σ with s ( sample...

This is not a homework problem so I'm asking it here. I just ran an MCMC and found the best fit parameters for a model of massive gravity. I now need to find the said 68% Confidence Interval interval for those parameters. I have never done anything like this before so I'm clueless where to begin...

I have a question regarding when to go for standard deviation σ or confidence interval ci. I am not sure of how to interpret ci. It seems to give me an option to choose the level of confidence, but I don't see why the the ci is divided by the root of the number of samples. Any pointers would be...

Hey! :o We have a 90%-confidence interval. I want to check if the following statements are correct. 1. If double the sample, the possibility that the value that we are looking for is out of the confidence interval is smaller. 2. The bigger the standard error, the smaller the confidence...

This is the word problem I am faced with... I have provided my answer. Please give input if I am right or wrong. It is 1581 Anno Domini. At the Undergraduate School of UMUC, besides Assistant Academic Director of Mathematics and Statistics, I am also the Undergraduate School-appointed CPA...

Hello Physicsforum Homework Statement I have a problem proving this: Given C(x)=[0, 3/x] for all x\in\chi, with \chi=\Omega being the sample space and P_q=Geom(q) being the geometric distribution. I have to show that C(x) is a confidence Interval for q but I don't know how to get started...

Hi, I’m having a problem with a particular case of binomial proportion. I want calculate a confidence Intervals for a binomial proportion for an efficiency. This kind of intervals are usually defined for ratios between integers numbers but in my case I had to subtract from both numerators and...

I run an algorithm that outputs a normally distributed random number with unknown mean and variance. I need to know the mean of those numbers. To do that, i repeatedly run that algorithm to obtain many numbers, then I calculate the mean and the confidence interval for the mean. Over the last...

I have a question I've been working on and I've noticed that my solution differs from the textbook solution. I would have considered it a mistake, but the next 4 questions are similar with the same solution "mistake"? Aside from not converting the % to 0.885, I am wondering about part b. It...

Hello! (Wave) Let $X_1, X_2, \dots, X_n$ a random sample with $E(X_i)=\mu$, $Var(X_i)=\sigma^2 \forall i$. For $0<a<0.5$: show that for any $k \in [0,1]$, the interval $$\left( \overline{X}-z_{k=a} \frac{\sigma}{\sqrt{n}}, \overline{X}+z_{(1-k)=a} \frac{\sigma}{\sqrt{n}}\right)$$ is a...

Homework Statement 1.) When we collect more data for our confidence interval (A) Confidence Increases (B) Confidence Decreases (C) n decreases (D) The length of the interval decreases (E) The length of the interval increases 2.) We wish to determine a confidence interval for the population...

Is it possible to predict an election outcome based on a confidence interval for the population proportion?

Homework Statement Some car tires can develop what is known as "heel and toe" wear if not rotated after a certain mileage. To assess this issue, a consumer group investigated the tire wear on two brands of tire, A and B, say. Fifteen cars were fitted with new brand A tires and thirteen with...

I am working on a problem for my Statistics class and I am looking for some clarification and some direction. The questions asks about a study that has been done on the diameter of 50 screws (both digital and vernier scale calipers). The differences in the measured diameters had the following...

Homework Statement A diet pill is given to 9 subjects over six weeks. The average difference in weight (follow up - baseline) is -2 pounds. What would the standard deviation have to be for the 95% T confidence interval to lie entirely below 0? ANSWER: Around 2.6 pounds or less Refer to the...

Homework Statement Latency Time(years): Number of patients 0: 2 1: 6 2: 9 3: 33 4: 49 5: 66 6: 52 7: 37 8: 18 9: 11 10: 4 (I don't know how to make a proper table with latex... tried \being{tabular}{l r} but this doesn't work) Homework Equations When the variance is...

Hello guys, I would like to calculate the confidence interval of the data in which the data is correct. In otherwords I would like to know how much confidence we have that the data is correct. Could anyone direct me where to start? Thank you.

Homework Statement Suppose that an investigator believes that virtually all values in the population are between 38 and 70. The appropriate sample size for estimating the true population mean within 2 units with 95% confidence level is approximately how much? Homework EquationsVariance of the...

Homework Statement Suppose you have a bucket containing a lot of balls with different colors. You randomly pick 50 balls, 9 of which are red (X = 9, where X ~ N(μ, σ²)). The probability of picking a red ball is 15%. From this you want to construct a 95% confidence interval for the standard...

Homework Statement Suppose X1, X2, ..., Xn constitute a random sample from a population following N(μ,θ) where μ is known. (a)Find a sufficient statistic for θ. (b)Use the maximum likelihood estimator of θ to construct a confidence interval for θ with confidence level 1-α. Homework...

Homework Statement What does it mean? Is this the interval such that 95% of the means from a sample mean distribution (frequency distribution of means of sample size n) are a certain number of standard deviations from the population mean? Homework Equations The Attempt at a Solution

The distribution of grades is know to follow a normal distribution, but the mean and variance are unknown. A random sample of 12 students produced the following scores: 59, 84, 68, 93, 49, 77, 82, 75, 81, 58, 70, 80 Find the 90% two-sided confidence interval for the mean score.

See attached for problem Working: Mean: 1203.26 Standard Deviation: 7.047 for 99% confidence interval, level of significance = 0.01 Therefore 0.5 - 0.01/2 = 0.45 Reading 0.45 from standard distribution table i get a value of 1.65 therefore confidence interval should be...

I have a bunch of noisy data points (x,y), and I want to model the data as y = ax2 + bx + c + noise where noise can probably be assumed to be Gaussian, or perhaps uniformly distributed. My data is firmly inside of an interval and I'm only interested in modeling correctly inside of this...

Hello May I know what is the difference between Confidence Interval for Population Mean (μ) when σ Known vs Confidence Interval for Population Mean (μ) when σ unknown.. any example to show me??

Hello, I need help using my TI 84 to figure out this 4 part question. My professor went over it way to quickly in class, when showing us how to do it on the TI 84, I believe its only a few quick steps for each part though. EDIT: I have figured out part d, but am still struggling with parts a...

A researcher surveys 25 people and finds that their average commute is 15 minutes with a standard deviation of 1.5 minutes. Calculate the 95 percent confidence interval on variance. Do most people have a commute of 20 minutes? Confidence interval for variance? should I just use the variance...

Homework Statement Let θ>0 and X1, X2,...,Xn be a random sample from the distribution with the pdf fx(x)=fx(x;θ)=(θ/(2√x))e-θ√x, x>0 Recall: Ʃ√xi, i=1, n has Gamma (α = n, "usual θ" = 1/θ) distribution. a) Suggest a confidence interval θ with (1-α)100% confidence level. b)...

Hi all. I've been thinking about this question a lot for the past few days and it seems to me that I'm committing a mistake somewhere along the way, but certainly can't figure out where. Here's one of the interpretations which I've encountered most frequently and think is the right one (here's...

Are there any online sources that would note (and define all variables, especially on how to calculate standard error) in the formula for calculating the confidence interval, a complement to the t-test, of two independent samples with unequal variances? (I want to see exactly how...