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# Sample Size, Sample Error, and Sum of Squares

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On average, what value is expected for the t statistic when the null hypothesis is true?
*1
*1.96
*0 (?)
*t>1.96

What is the sample variance and the estimated standard error for a sample of n=9 scores with SS= 72?
*s2=3 and sM=3
*s2 and sM= 1
*s2=9 and sM=3 (?)
*s2=3 and sM=1

Which set of characteristics will produce the smallest value for the estimated standard error?
*A large sample size and a small sample variance
*A large sample size and a large sample variance
*A sample sample size and a large sample variance
*A small sample size and a small sample variance (?)

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df=30, how many individuals were in the sample?
*n=30
*cannot be determined from the information given
*n=29 (?)
*n=31

When n is small (less than 30) how does the shape of the t distribution compare to the normal distribution?
* It is taller and narrower than the normal distribution
* It is almost perfectly normal
*There is no consistent relationship between the t distribution and the normal distribution.
*It is flatter and more spread out than the normal distribution . (?)

With o= .01, the two tailed critical region for a t test using a sample of n=16 subjects would have boundaries of :
*t= ±2.602
*t= ± 2.921
*t=± 2.947
*t= ± 2.583

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https://brainmass.com/statistics/hypothesis-testing/sample-size-sample-error-sum-squares-585148

#### Solution Preview

On average, what value is expected for the t statistic when the null hypothesis is true?
choose 0

What is the sample variance and the estimated standard error for a sample of n=9 scores with SS= 72?
choose s2=9 and sM=3 ...

#### Solution Summary

The solution gives detailed steps on discussing the relationship between sample size, sample error, and sum of squares.

\$2.19

## ANOVA tables for description of problems.

Fill in the missing entries using a one-way ANOVA table.

Source DF SS MS=SS/df F- statistic
Treatment 2.124 0.708 0.75
Error 20
Total

Construct the one way ANOVA table for the data. Compute SSTR and SSE using the defining formula:
SST = sum(x-xbar) squared
SSTR = sum of size of sample from population (mean of sample from population - xbar) squared
SSE = sum(size of sample from population - 1) variance of sample from population
Northeast Midwest South West
905 870 911 865
798 748 650 852
848 699 881 930
1081 814 1056 766
1144 721 1109
606
Note - Xbar1 = 955.2, xbar2 = 743.0, xbar3 = 874.5, xbar4 = 904.4
Variance1 = 22,548.7, Varaiance2 = 8,476.8, Variance3 = 28,239.0, Variance4 = 16,492.3 and xbar = 862.7

See attched ANOVA tables for description of problems.

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