Imagine that we have taken samples from a pair of populations and we're using an unpaired homoscedastic t-test to determine whether their means are equal or not. Q1. If the sample sizes are both 6 and the sample variances are 9, what is the minimum difference between the sample means we would need to observe to decide that the population means are significantly different? Q2. If the sample sizes are both 12 and the sample variances are 9, what is the minimum difference between the sample means we would need to observe to decide that the population means are significantly different? Q3. Imagine a pair of populations with standard deviations of 3.1 and means that differ. If we take a pair of samples of equal size which give us the exact same standard deviation and mean values as the population, and we're using an unpaired homoscedastic t-test, what is the minimum number of data values in each sample to detect a difference of 2.4? (Provide this to the nearest integer) Min. diff. = ??? Min. diff. = ??? Min. n = ???

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Enter all non-integer values to the nearest 0.001.
Imagine that we have taken samples from a pair of populations and we're using an unpaired homoscedastic
t-test to determine whether their means are equal or not.
Q1. If the sample sizes are both 6 and the sample variances are 9,
what is the minimum difference between the sample means we
would need to observe to decide that the population means are
significantly different?
Q2. If the sample sizes are both 12 and the sample variances are 9,
what is the minimum difference between the sample means we
would need to observe to decide that the population means are
significantly different?
Q3. Imagine a pair of populations with standard deviations of 3.1 and means
that differ. If we take a pair of samples of equal size which give us the exact
same standard deviation and mean values as the population, and we're using
an unpaired homoscedastic t-test, what is the minimum number of data values
in each sample to detect a difference f 2.4?
(Provide this to the nearest integer)
Min. diff. = ???
Min. diff. = ???
Min. n = ???
Transcribed Image Text:Prepare your answers and be ready to copy/paste Enter all non-integer values to the nearest 0.001. Imagine that we have taken samples from a pair of populations and we're using an unpaired homoscedastic t-test to determine whether their means are equal or not. Q1. If the sample sizes are both 6 and the sample variances are 9, what is the minimum difference between the sample means we would need to observe to decide that the population means are significantly different? Q2. If the sample sizes are both 12 and the sample variances are 9, what is the minimum difference between the sample means we would need to observe to decide that the population means are significantly different? Q3. Imagine a pair of populations with standard deviations of 3.1 and means that differ. If we take a pair of samples of equal size which give us the exact same standard deviation and mean values as the population, and we're using an unpaired homoscedastic t-test, what is the minimum number of data values in each sample to detect a difference f 2.4? (Provide this to the nearest integer) Min. diff. = ??? Min. diff. = ??? Min. n = ???
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