Confidence interval Definition and 102 Threads

Homework Statement A machine produces metal pieces that are cylindrical in shape. A sample of pieces is taken and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, 1.03 centimeters. Find a 99% confidence interval for the mean diameter of pieces from this machine...

To calculate the 95% confidence interval of the mean of a normal distribution you calculate 1.96 χ standard error on the mean. what do you do if you want to calculate the 95% confidence interval on the median of the distribution, for a distribution that is most definitely skewed and not...

So I have a research problem and I am not very good at statistics. I need to amplify a library of dna molecules with a set number of dna species and transform them into a organism. Basically, I need to know how many moles of the library I need in order to be confident that I am getting at least...

Homework Statement I have 20 data points of the surface roughness of oil pipes, the mean, and the std of the sample. I need to get a 95% confidence interval of the mean surface roughness of these pipes. I did a boxplot, and found that it's negatively skewed, and therefore not normally...

Homework Statement Assume Y1, ... , Yn is a sample of size n from a gamma distributed population with α = 2 and unknown β a) Use the method of moment generating functions to show that U = 2 \sum_1^n Y_i / β is a pivotal quantity and has a chi-square distribution with 4n d.f. b)...

Hello, Let me get right to my problem. I have an experimental distribution and a single-parameter theoretical distribution. I want to find the value for the best fit theoretical distribution that agrees with my experimental data for the bulk of the distributions (the tails of my...

Homework Statement 1a) Data x1, x2, ...xn are modeled as observations of independent random variables each having the Gaussian distribution with unknown mean  μ and unknown variance σ2. Suppose that n = 10, Ʃxi = 5 and Ʃxi2= 42:5. Look up the value of the 95% percentile of a t-...

Homework Statement (I translated this from french) Some n dice are thrown and the sum of all their face values is 117. Estimate n through a confidence interval of 90%. In other words, of all the possible rolls of n dice that sum up to 117, find a range in which n should be located 90%...

Homework Statement In a primary school, the mean height of the students of primary 1 students is 120cm. Given a sample size of 40, the confidence interval is 117 and 123. Find the confidence interval if the sample size is 30 instead. Homework Equations Standard deviation and confidence level...

Homework Statement X1,...Xn is a random sample from N(μ, σ^2) Homework Equations Estimator of μ maybe? a1 + a2 = a a1 = a2 = a/2 (x-μ)/(σ/√n)~N(0,1) ((x-μ)/σ)^2~Chi square(1) The Attempt at a Solution I tried to replace μ with its estimator xbar but that gives me 0.

Homework Statement Homework Equations The Attempt at a Solution

The following are summary statistics for a data set. Would it be appropriate to use the Student's t- distribution to construct a confidence interval for these data? Explain clearly! Sample size = 10 Mean = 8.905 Median = 6.105 Standard deviation = 9.690 Minimum = 0.512 Maximum = 39.920...

The following are summary statistics for a data set. Would it be appropriate to use the Student's t- distribution to construct a confidence interval for these data? Explain clearly! Sample size = 10 Mean = 8.905 Median = 6.105 Standard deviation = 9.690 Minimum = 0.512 Maximum = 39.920...

Say that there is a random variable X ~ U(a,b) where U is the discrete uniform distribution on integers on the interval [a,b]. Sample n such variables with the same (unknown) parameters a and b. Using those samples it's possible to estimate the mean either by taking the sample mean (sum the...

Hello, I'm doing some nonlinear regression fitting, and I have a set of data with n data points and I am fitting the data to a model which contains 3 parameters. I can get a confidence interval from the program I'm using for each parameter, but how can I calculate the standard deviation for...

Homework Statement Janet sells cookware at home parties, she wants to estimate the average amount a client spends at each party. A random sample of 35 receipts gave a mean of X bar = $34.70 with standard deviation s = %4.85. a) find a 90% confidence interval for the average amount spent by...

Homework Statement I'm doing a past paper for my statistics course, and there's no provided solutions. I want to know if my attempt is correct. This is part of the paper: Homework Equations N/A The Attempt at a Solution i) Q0 = 1.06, Q1 = 1.335, Q2 = 2.04, Q3 = 2.275, Q4 = 2.64 ii) IQR = Q3...

Homework Statement Let X1, X2,...Xn be a random sample from the distribution with probability density function fX (x;θ) = (θ+1)(1-x)θ, 0<x<1 θ>-1 a) What is the probability distribution of Y= -\sum ln(1-Xi from i=1 -> n b) Suggest a (1-α)100% confidence interval for θ based on Y=...

Homework Statement There's no need to write out the full question, but basically we have 6 diets, and for each one a list of the levels of protein in 10 independant samples for each. Sample mean and standard deviation given. Calculate and interpret a confidence interval centered on the...

From Koosis, I pieced together the following algorithm. Is sigma known? Yes? Then calculate the exact confidence interval using a normal distribution to estimate that of the sample means, with mean = the mean of sample means = the mean of the population, \mu_{\overline{x}}=\mu, and...

My course notes and textbook express this differently: To construct the confidence interval for diff. between means, Course notes (\bar{x1} - \bar{x2})\pmE Textbook (\bar{x1} - \bar{x2}) - E < \mu1 - \mu2 < (\bar{x1} - \bar{x2}) + E why the difference?

Homework Statement You look at a random sample of 64 vehicles in one school parking lot and find that 24 are trucks. Determine the 80% confidence interval for the true population proportion of trucks in all the school lots. Homework Equations (work shown below) The Attempt at a...

I am trying to calculate the confidence interval for this problem using my T-84, and it's driving me mad because I'm so close to the correct answer. The problem is Homework Statement The answer to this problem is (22769.83, 30059.41) (This is an example problem.) When I try to duplicate...

Homework Statement in 225 out of 2700 schools, the number of registrations were recorded. The average was 3700, and the standard deviation 6000. Give the 95% confidence interval for the total number of registrations in all of the 2700 schools.Homework EquationsThe Attempt at a Solution I first...

So as the title says. How do you calculate the confidence interval that is not on the t-table. For example how do you calculate the confidence interval for 97%? Assume that it is a normal distribution, you are not given σ and that n<30. Is there a formula? Or should i look for a more specific...

Homework Statement Twenty-eight children were given a language test with the scores recorded on a scale of 0 to 100. The variance in the test scores serves as a measure of the homogeneity in language skills for children. The sample standard deviation of the test scores was found to be 12...

I got a question which has been confused me for a long time. The question is to calculate the 95% confidence interval for a curve. I have already learned how to calculate for a straight line. For example, the cumulative distribution function (CDF) could be expressed as below: Y = 1/2 * {1...

when we calculate a value, say @95% we get 9.99+- .002 this value is describing a parameter of the true population right? it is not saying 95% of the time we get samples, it will fall in this range correct? We never infer anything about statistics, only parameters of populations right...

Homework Statement I re-wrote a previous thread just to make it clearer: Construct a normal symmetric 100(1-alpha)% confidence interval [L,R] for p then show that [L,1] is then an approximate 100(1-alpha/2)% confidence interval for p The normal distribution ranges from 0 to 1 The...

How would you go about finding the confidence interval for the parameters of the gamma distribution? I have had a look online and haven't found anything with the answer... Thanks

Homework Statement 1000 samples each of size n=121, where observations Xi ~ iid N ( m, sigma^2), for each sample we calculate Confidence Interval: I = [ 0.75 s^2, s^2 + s^2/4 ] where s^2=(1/(n-1))\Sigma(Xi-X bar)^2 how many samples include the true value of sigma^2, ie 1000 * prob...

Homework Statement What formula do I need to find the confidence interval, when I have got: - Number of samples - Level of Confidence - The assumed (1st guess) accuracy Homework Equations I found the following equation online: µ = z * [p * (1 - p) / n] ^ (-1/2) The Attempt at...

I a survey, out of 530 women and 509 men, 10.4% of the women and 21.6% of the men answered yes to a question. Calculate a 99% CI for the difference between two times the population proportion women and the population proportion men who answered "yes". Answer from book: (-0.091;0.075)...

I have a set of data that consists of about ~1000 data points, each of which has two measurements. I have a series of models with two parameters that I have fit to this data to find the best fitting pair of parameters. There is quite a spread around the best-fitting model, because none of the...

I have data that I want to fit to both Gaussian and Lorentzian (Cauchy) distribution. I have been using Matlab's nlinfit as follows: gaus = @(p,xdata) (p(1)/(sqrt(2*pi*p(2)))*exp(-(xdata-p(3)).^2/(2*p(2)))+min).*weights; [g_pfit,g_residual,g_J]=nlinfit(data(:,1), data(:,2).*weights, gaus...

A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured(a display ad is a large block of multicolored illustrations, maps, and text). The data (in square...

I don't know which forum to put this in... So here goes. Homework Statement Basically, I have gathered 30 data points that vary from about 1.3 - 4.7 in value (it doesn't matter what it is) with a mean of 2.98. Since I haven't done any statistics courses yet, I used the built in Excel...

How would you find CI for some function of a parameter? the case I'm particularly interested in is an approximate CI for p^2 where p is the proportion in the binomial model. http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval

Hi, if I have the confidence interval for the point estimate of an option price A which was found through simulation, can I also find a confidence interval for delta (dA/dS), where S is underlying asset price, without further simulation? thanks, sl

Homework Statement http://www.geocities.com/asdfasdf23135/stat15.JPG I am OK with part a, but I am having some troubles with part b. Homework Equations Width of a Confidence Interval The Attempt at a Solution Attempt for part b: http://www.geocities.com/asdfasdf23135/stat16.JPG...

The following distinguishes TWO cases for large samples confidence interval for difference in means: http://www.geocities.com/asdfasdf23135/stat11.JPG where Sp^2 is the pooled estimate of the common variance, n1 is the sample size from the first population, n2 is the sample size from the...

Let's say we know this: \sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right) How do we get from this information to this expression of confidence interval for \theta? \left( \widehat{\theta} \pm...

I am trying to calculate the chi squared function for life data and a confidence level of 95%. I have 10 data points, a specified confidence level (95%), and 1 degree of freedom. I also have the alpha and beta parameters. Based on this information how can i calculate the chi squared statistic? I...

What's the probability that a confidence interval (with alpha=10%), will have at least 85 of 100 predicted means within the calculated interval range (xbar +/- 1.645(sigma/sqrt(n)))? I understand that on average 90% of my means will be located in this range (and I know how to find this...

Lets say you have 5 trials, and 5 output let's say {5, 43, 60, 30 , 4}...so how would u get the chi sqaure from here & the confidence interval. i haven't work on prob &statc in years, thanks a lot for help folks

Lets say you have 5 trials, and 5 output let's say {5, 43, 60, 30 , 4}...so how would u get the chi sqaure from here & the confidence interval. i haven't work on prob &statc in years, thanks a lot for help folks

A container of oil is supposed to contain 1000 ml of oil. We want to be sure that the standard deviation of the oil container is less than 20 ml. We randomly select 10 cans of oil with a mean of 997 ml and a standard deviation of 32 ml. Using these sample construct a 95% confidence interval...

[Solved]Is a stats question,just need some clarity on it-"total width of less than 2. Homework Statement Hi.The result of a memory test is known to be normally distributed with mean mew and standard deviation 1.0. It's required to have a 95% confidence interval for mew with a total width of...

(Moving this to another section, because it is not for a particular course ...) I'd greatly appreciate any direction toward establishing the result below. I am studying statistics on my own, and found this in some online materials, but it didn't come with a solution, and I've been a bit...

Hi, I am an 3rd engineering student working on my coop report. My job was to design routes for survey work, and come up with figures of potential time savings if this was to be done on a grand scale. The sites are divided into 15 regions (by geography) but are not in any particular order...