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Computing Pooled Variance and Standard Error for 2 Sample Means

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Two separate samples, each with n=15 individuals, receive different treatments. After treatment, the first sample has SS=1740 and the second has SS=1620.
The pooled variances for the two samples is _________.
Compute the estimated standard error for the sample mean difference.
Estimated s(M1-M2)=________
If the sample mean difference is 8 points, is this enough to reject the null hypothesis and conclude that there is a significant difference for a two tailed test at the .05 level?
* Fail to reject the null hypothesis; there is no significant difference.
* Reject the null hypothesis; there is a significant difference.
* Fail to reject the null hypothesis; there is a significant difference.
* reject the null hypothesis; there is no significant difference.

t - critical = ±_________
t= ________

Assume that the two samples are obtained from populations wight the same mean, and calculate how much difference should be expected, on average, between the two sample means.
Each sample has n=4 with s2=68 for the first sample and s2= 76 for the second. ________
Each sample has n=16 scores with s2=68 for the first sample and s2=76 for the second. ______
In the second part of this question, the two samples are bigger than in the first part, but the variances are unchanged. How does the sample size affect the size of the standard error for the sample mean difference?
* As sample size increases, standard error remains the same.
* As sample size increases, standard error increases
* As sample size increases, standard error decreases.

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The pooled variances for the two samples is ___(1740+1620)/(15-1+15-1)=120______.

Estimated s(M1-M2)=___sqrt[120*(1/15+1/15)]=4_____

If the sample mean difference is 8 points, is this enough ...

Solution Summary

The solution gives detailed steps on computing pooled variance, standard error for two sample means and explaining relevant hypothesis testing problem.

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1. Several factors influence the value obtained for a t statistic. Some factors affect the numerator of the t statistic and others influence the size of the estimated standard error in the denominator. For each of the following, indicate whether the factor influences the numerator or dominator of the t statistic and determine whether the effect would be to increase the value of t (farther from zero) or decrease the value of t (closer to zero). In each case, assume that all other factors remain constant.
a. Increase the variability of the scores.
b. Increase the number of scores in the sample.
c. Increase the difference between the sample mean and the population mean.

2. The following sample was obtained from a population with unknown parameters.
Scores: 1, 5, 1, 1
a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data).
b. Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean).

3. A sample of n = 25 individuals is randomly selected from a population with a mean of u = 65, and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 70.
a. If the sample standard deviation is s = 10, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with x = .05?
b. If the sample standard deviation is s= 20, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with x = .05?

4. The herbal supplement ginkgo biloba is advertised as producing an increase in physical strength and stamina. To test this claim, a sample of n = 36 adults is obtained and each person is instructed to take the regular daily dose of the herb for a period of 30 days. At the end of the 30-day period, each person is tested on a standard treadmill task for which the average, age-adjusted score is u = 15. The individuals in the sample produce a mean score of M = 16.9 with SS = 1260.
a. Are these data sufficient to conclude that the herb has a statistically significant effect using a two-tailed test with x = .05?
b. What decision would be made if the researcher used a one-tailed test with x = .05 ? (Assume that the herb is expected to increase scores.)

5. What is measure by the estimated standard error that is used for the independent-measure t statistic?

6. One sample has SS = 35 and a second has SS = 45.
a. Assuming that n= 6 for both samples, calculate each of the sample variances, then calculate the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances.
b. Now assume that n = 6 for the first sample and n = 16 for the second. Again, calculate the two sample variances and the pooled variance. You should find that the pooled variance is closer to the variance for the larger sample.

7. One sample has n = 4 scores with SS = 100 and a second sample has n = 8 scores with SS = 140.
a. Calculate 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 6 points, is this enough to reject the null hypothesis for a two-tailed test with x = .05?
d. If the sample mean difference is 9 points, is this enough to reject the null hypothesis for a two-tailed test with x = .05?

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