Statistics for The Behavioral Scie...

10th Edition

Frederick J Gravetter + 1 other

ISBN: 9781305504912

Textbook Problem

Two separate samples receive different treatments. After treatment, the first sample has n = 9 with S S = 462 , and the second has n = 7 with S S = 420 .

a. Compute the pooled variance for the two samples.

b. Calculate the estimated standard error for the sample mean difference.

c. If the sample mean difference is 10 points, is this enough to reject the null hypothesis using a two-tailed test with α = .05 ?

To determine

Sample variances, Pooled variance, standard error of mean difference, also we need to take decision that a difference of mean is significant or not.

Explanation

Here we have given with different two SS and we need to find variance as well as pooled variance so here we will use general formula so that we can use for any two different sample size.

Here we need to find that the standard error of mean difference that will be described that how far is the distance of the two means of the sample from the population difference. Also we have testing in the part c there will be decide that whether true difference is 10 or not basis of sample data we have.

Given:

Here we are provided with two SS that is SS₁=462 and SS₂= 420, also for

n₁=9, n₂=7

Formula used:

For one sample of size n, we have below formulas

Mean= x¯ = 1n∑i=1nxi

SS= ∑i=1n(xi−x¯)2

Variance= 1n−1∑i=1n(xi−x¯)2

If there are two samples of sizes n₁and n₂ we have the following formula for pooled SD,

S_p=Pooled Variance

SP=(n1−1)×s12+(n2−1)×s22(n1+n2−2)

S₁²=sample variance of first sample

S₂²=sample variance of second sample

Denote,

S_e=standard error of the mean,

Se=Sp1n1+1n2

Calculation:

Here

n1=9,n2=7 So now

s12=1n1−1∑i=1n1(x1i−x1¯)2=4629−1=57

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Statistics Statistics for The Behavioral Sciences (MindTap Course List)10th Edition