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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A researcher is using an independent-measures design to evaluate the difference between two treatment conditions with n = 8 in each treatment. The first treatment produces M = 63 with a variance of s2 = 18, and the second treatment has M = 58 with s2 = 14.

a. Use a one-tailed test with α = .05 to determine whether the scores in the first treatment are significantly greater than the scores in the second. (Note: Because the two samples are the same size, the pooled variance is simply the average of the two sample variances.)

b. Predict how the value for the t statistic would be affected if the two sample variances were increased to s2 = 68 and s2 = 60. Compute the new t to confirm your answer.

c. Predict how the value for the t statistic for the original samples would be affected if each sample had n = 32 scores (instead of n = 8). Compute the new t to confirm your answer.

a.

To determine
Whether the scores in the first treatment significantly greater than the scores in the second treatment.

Explanation

Given info:

Two samples each of size 8 has means 63 and 58 respectively. The variances for the two samples are 18 and 14 respectively.

Calculation:

Step 1: Null hypothesis is H0:μ1μ20 and

            Alternate hypothesis is H1:μ1μ2>0

Step 2: For the given sample, t-statistics will have degree of freedom equals:

df=n1+n22=8+82=14

For one-tailed test with α=0.05 and df=14, the critical value (CV) is obtained from the t-table as t=1.761

Step 3: t-statistics is obtained as below,

Pooled variance sp2:

sp2=SS1+SS2df1+df2

Where,

SS1=s12(n11)=18(81)=126

Ss2:

SS2=s12(n21)=14(81)

b.

To determine

To predict: The effect of the value in t-statistic if the two sample variances are increased.

To compute: The new t.

c.

To determine

To predict: The effect of the value in t-statistic if the values of sample sizes increased to 32.

To determine: Whether the above prediction is correct or not by finding the t value.

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