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 = .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.
Two samples each of size 8 has means 63 and 58 respectively. The variances for the two samples are 18 and 14 respectively.
Step 1: Null hypothesis is and
Alternate hypothesis is
Step 2: For the given sample, t-statistics will have degree of freedom equals:
For one-tailed test with and the critical value (CV) is obtained from the t-table as
Step 3: t-statistics is obtained as below,
Pooled variance :
To predict: The effect of the value in t-statistic if the two sample variances are increased.
To compute: The new t.
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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