# Sample Size, Sample Error, and Sum of Squares

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

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.

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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