Penn State Statistics
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Lesson 3: Confidence Intervals for Two Means
Three assumptions are made in deriving the above confidence interval formula. They are: The measurements ( \(X_i\) and \(Y_i\)) are independent. The measurements in each population are normally distributed. The measurements in each population have the same variance \(\sigma^2\). That means that we should use the interval to estimate the difference in two population means only when the three conditions hold for our given data set.
Boston University
sphweb.bumc.bu.edu › otlt › mph-modules › bs › bs704_confidence_intervals › bs704_confidence_intervals5.html
Confidence Interval for Two Independent Samples, Continuous Outcome
In the two independent samples application with a continuous outcome, the parameter of interest is the difference in population means, μ1 - μ2. The point estimate for the difference in population means is the difference in sample means: The confidence interval will be computed using either the Z or t distribution for the selected confidence level and the standard error of the point estimate.
Videos
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PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC3699740
Confidence intervals for two sample means: Calculation, interpretation, and a few simple rules - PMC
Here, a typical description to be used in a figure caption would be “Error bars represent the XY% confidence interval of the individual means” or, to use the suggested nomenclature, a similar statement on the axis of a graph (e.g., “RT ± SEM” or “RT and CIM”). These error bars inform about the homogeneity of variance across different samples or conditions and - even though they cannot be used for inferences about the difference between two means - they provide information about the difference of each mean from a fixed parameter.
Socscistatistics
socscistatistics.com › confidenceinterval › default4.aspx
Confidence Interval Calculator: Independent Samples T-Test
This simple confidence interval calculator uses a t statistic and two sample means (M1 and M2) to generate an interval estimate of the difference between two population means (μ1 and μ2).
Calcworkshop
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Confidence Interval for Difference in Means w/ 7 Examples!
Depending on the sample types and whether or not the population standard deviation is known will depend on whether we employ either a z-test or t-test. Suppose the population standard deviation is known, which is highly unlikely. In that case, we will use a z-test and follow the following formula for constructing a confidence interval for the difference of means. ... But for two independent random samples where the standard deviation is unknown, and the sample size is sufficiently large, then we will have to use a t-test, which involves a t-distribution with degrees of freedom, as well as the possibility of pooled variances.
Published October 10, 2020
Lumen Learning
courses.lumenlearning.com › wm-concepts-statistics › chapter › estimating-the-difference-in-two-population-means
Estimating the Difference in Two Population Means | Concepts in Statistics
In this example, we use the sample data to find a two-sample T-interval for μ1 − μ2 at the 95% confidence level.
NCSS
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PASS Sample Size Software NCSS.com 471-1 © NCSS, LLC. All Rights Reserved.
Upper and lower one-sided confidence intervals can be obtained by replacing α/2 with α. ... The required sample size for a given precision, D, can be found by solving the following equation iteratively · 𝐷𝐷= 𝑡𝑡1−𝛼𝛼/2,𝑛𝑛1+𝑛𝑛2−2𝑠𝑠𝑝𝑝ඨ1 ...
StatsKingdom
statskingdom.com › difference-confidence-interval-calculator.html
Calculates the confidence interval for the difference between two means - with calculation steps
CL -confidence level α = 1 - CL. T1 - α/2 - the t-score based on the t distribution, p(t < T1 - α/2) = 1 - α/2. df - degrees of freedom. The following R code should produce the same results. Find the means' difference confidence interval in the t.test results.
Dummies
dummies.com › article › academics-the-arts › math › statistics › how-to-create-a-confidence-interval-for-the-difference-of-two-means-with-unknown-standard-deviations-andor-small-sample-sizes-169794
How to Create a Confidence Interval for Difference of Two Means ...
July 2, 2025 - In either of these situations, a confidence interval for the difference in the two population means is · where t* is the critical value from the t-distribution with n1 + n2 – 2 degrees of freedom; n1 and n2 are the two sample sizes, respectively; ...
GIGACalculator.com
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Confidence Interval Calculator
The formula when calculating a one-sample confidence interval is: where n is the number of observations in the sample, X (read "X bar") is the arithmetic mean of the sample and σ is the sample standard deviation (&sigma2 is the variance). The formula for two-sample confidence interval for ...
Dummies
dummies.com › article › academics-the-arts › math › statistics › creating-a-confidence-interval-for-the-difference-of-two-means-with-known-standard-deviations-169797
Creating a Confidence Interval for the Difference of Two Means ...
July 2, 2025 - Call the two varieties Corn-e-stats and Stats-o-sweet. Assume by prior research that the population standard deviations for Corn-e-stats and Stats-o-sweet are 0.35 inches and 0.45 inches, respectively. Because you want a 95 percent confidence interval, your z* is 1.96. Suppose your random sample of 100 cobs of the Corn-e-stats variety averages 8.5 inches, and your random sample of 110 cobs of Stats-o-sweet averages 7.5 inches.
Calculator.net
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Confidence Interval Calculator
Calculating a confidence interval involves determining the sample mean, X̄, and the population standard deviation, σ, if possible. If the population standard deviation cannot be used, then the sample standard deviation, s, can be used when the sample size is greater than 30.
StudySmarter
studysmarter.co.uk › confidence interval for the difference of two means
Confidence Interval for the Difference of Two Means |StudySmarter
Let's look at an example of applying these formulas and drawing conclusions. You do a survey of \(40\) small town coffee shops and \(49\) big city coffee shops, and find that the mean price of a large cup of coffee is \(\$3.75\) and in the big cities it is \(\$ 4.50\). You also know that the sample standard deviation in small towns is \(1.00\), and in big cities the sample standard deviation of \(0.70\). Construct a \(99\%\) confidence interval for the difference of their two means, and draw conclusions from it.
Penn State Statistics
online.stat.psu.edu › stat415 › lesson › 3 › 3.1
3.1 - Two-Sample Pooled t-Interval | STAT 415
Three assumptions are made in deriving the above confidence interval formula. They are: The measurements ( \(X_i\) and \(Y_i\)) are independent. The measurements in each population are normally distributed. The measurements in each population have the same variance \(\sigma^2\). That means that we should use the interval to estimate the difference in two ...
Penn State Statistics
online.stat.psu.edu › stat100 › lesson › 9 › 9.3
9.3 - Confidence Intervals for the Difference Between Two Population Proportions or Means | STAT 100
Similarly for the men in the study the SEM for the right-left strength differential is\(\frac{3.6}{\sqrt{60}}=0.465\) and a 95% Confidence Interval for the average strength differential in the population of men is 4.7 kg ± 2(0.465) kg or 4.7 kg ± 0.93 kg. The interval goes from 3.77 kg up to 5.63 kg. Finally, we want to examine the idea that the right-left strength differential will be different between the 30-39 year old men and the boys < 10. That comparison involves two independent samples of 60 people each.
Statology
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Confidence Interval for the Difference Between Means
June 23, 2020 - Confidence interval = (x1–x2) +/- t*√((sp2/n1) + (sp2/n2)) ... Suppose we want to estimate the difference in mean weight between two different species of turtles, so we go out and gather a random sample of 15 turtles from each population.
Stats
stats.blue › Stats_Suite › two_sample_t_confidence_interval.html
Two-Sample t Confidence Interval
The two-sample $t$ procedures assume that both our samples come from an SRS and will give trustworthy conclusions only if this condition is met.
Statistics LibreTexts
stats.libretexts.org › bookshelves › introductory statistics › mostly harmless statistics (webb) › 9: hypothesis tests and confidence intervals for two populations
9.2: Two Independent Groups - Statistics LibreTexts
March 12, 2023 - For an interpretation, if we were to use the same sampling techniques, approximately 95 out of 100 times the confidence interval (0.2813, 0.5187) would contain the population mean difference in voltage between alkaline and NiMH batteries. Since both endpoints are positive, we can reject H0. We can be 95% confident that the population mean voltage for alkaline batteries is between 0.28 and 0.52 volts higher than nickel metal hydride batteries. There is no shortcut option for a two-sample z confidence interval in Excel.
ThoughtCo
thoughtco.com › sample-t-test-confidence-interval-example-4022456
Two Sample T-Tests and Confidence Intervals
May 1, 2025 - Formula for Student's t distribution. ... Courtney K. Taylor, Ph.D., is a professor of mathematics at Anderson University and the author of "An Introduction to Abstract Algebra." ... The two-sample t-test checks if fifth graders' mean scores are higher than third graders'. A 95% confidence interval tells us how much better fifth graders might do than third graders.
JMP Statistical Discovery
jmp.com › en › learning-library › topics › basic-inference-proportions-and-means › two-sample-t-test-and-confidence-interval
Two Sample t-Test and Confidence Interval
Test a hypothesis and generate a confidence interval comparing two population means.