# Small sample test for the difference between two means

• Poke
And my calculated value of p is about 0.8.) So, no worries.In summary, the article "Variance Reduction Techniques: Experimental Comparison and Analysis for Single Systems" (I.Sabuncuoglu, M. Fadiloglu, and S. Celik, IIE Transactions, 2008:538-551) compares the effectiveness of the method of Latin Hypercube Sampling in reducing the variance of estimators for the mean time-in-system in two queueing models: M/M/1 and serial line. The study found that for both models, ten replications resulted in average reductions of 6.1 and 6.6, respectively, with standard deviations of 4.1 and
Poke

## Homework Statement

The article “Variance Reduction Techniques: Experimental Comparison and Analysis for Single Systems” (I.Sabuncuoglu,M. Fadiloglu, and S. Celik, IIE Transactions, 2008:538–551) describes a study of the effectiveness of the method of Latin Hypercube Sampling in reducing the variance of estimators of the mean time-in-system for queueing models. For the M/M/1 queueing model, ten replications of the experiment yielded an average reduction of 6.1 with a standard deviation of 4.1. For the serial line model, ten replications yielded anaveragereductionof6.6withastandarddeviationof 4.3. Can you conclude that the mean reductions differ between the two models?

## Homework Equations

nx = 10 ; X= 6.1 ; Sx = 4.1
ny = 10 ; Y= 6.6 ; Sy = 4.3

H0: X-Y = 0 ; H1: X-Y ≠0 ; Δ0 = 0

As we cannot assume standard deviations to be equal, we use the formula that find student's t and the degree of freedom v.

## The Attempt at a Solution

It is found that v = 17.959, rounded down to 17
with t calculated as 0.2661

As H1: X-Y ≠0, P is the sum of cutoffs
We are to find Alpha, based on v = 17 and t' = 2t = 0.5322
It is founded that alpha between 0.25 and 0.40

All of which higher than 5%, so H0 is not rejected, and cannot conclude the mean reductions differ between the two models.My approaches correct, as well as the answer make sense? Thanks!

Not sure why you doubled t to t' = 2t = 0.5322 rather than using t directly. Do you have a reference for that? (I don't think that Welch's t-test does that.)

Your final conclusion of no significant difference certainly makes sense. A rough "guestimate" of the 95% confidence interval on the first sample puts the second sample mean well within the interval.

Last edited:

## 1. What is a small sample test for the difference between two means?

A small sample test for the difference between two means is a statistical tool used to determine whether there is a significant difference between the means of two populations based on a small sample size. It is typically used when the sample size is less than 30 and the population standard deviations are unknown.

## 2. When should a small sample test for the difference between two means be used?

A small sample test should be used when the sample size is small and the standard deviations of the populations are unknown. This is because other tests, such as the t-test, may not be reliable in these situations.

## 3. How is a small sample test for the difference between two means performed?

To perform a small sample test for the difference between two means, the first step is to calculate the difference between the means of the two samples. Then, the standard error of the difference is calculated using the sample standard deviations and sample sizes. Finally, this standard error is used to calculate the test statistic and determine the p-value, which is compared to a significance level to determine if the difference between the means is statistically significant.

## 4. What is the significance level in a small sample test for the difference between two means?

The significance level, also known as alpha, is the predetermined probability at which the null hypothesis is rejected. It is typically set at 5% or 0.05, meaning that if the calculated p-value is less than 0.05, the difference between the means is considered statistically significant and the null hypothesis is rejected.

## 5. What is the null hypothesis in a small sample test for the difference between two means?

The null hypothesis in a small sample test for the difference between two means states that there is no significant difference between the means of the two populations. The alternative hypothesis, on the other hand, states that there is a significant difference between the means. The goal of the test is to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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