Question

The MINITAB printout shows a test for the difference in two population means.

Two-Sample T-Test and CI: Sample 1, Sample 2
Two-sample T for Sample 1 vs Sample 2
     N Mean StDev SE Mean
Sample 1 6 28.00 4.00 1.6
Sample 2 9 27.86 4.67 1.6
Difference = mu (Sample 1) - mu (Sample 2)
Estimate for difference: 0.14
95% CI for difference: (-4.9, 5.2)
T-Test of difference = 0 (vs not =):
T-Value = 0.06 P-Value = 0.95 DF = 13
Both use Pooled StDev = 4.42

(a) Do the two sample standard deviations indicate that the assumption of a common population variance is reasonable?
Yes, the ratio of the two variances is less than three.Yes, the ratio of the two variances is more than three.    No, the ratio of the two variances is less than three.No, the ratio of the two variances is more than three.It is not possible to check that assumption with the given information.
(b) What is the observed value of the test statistic?
t =  

What is the p-value associated with this test?
p-value =  

(c) What is the pooled estimate s2 of the population variance? (Round your answer to two decimal places.)
s2 =  

(d) Use the answers to part (b) to draw conclusions about the difference in the two population means. (Use ? = 0.10.)
Since the p-value is greater than 0.10, the results are not significant. There is insufficient evidence to indicate a difference in the two population means.Since the p-value is greater than 0.10, the results are significant. There is sufficient evidence to indicate a difference in the two population means.    Since the p-value is less than 0.10, the results are significant. There is sufficient evidence to indicate a difference in the two population means.Since the p-value is less than 0.10, the results are not significant. There is insufficient evidence to indicate a difference in the two population means.
(e) Find the 95% confidence interval for the difference in the population means.
to  

Does this interval confirm your conclusions in part (d)?
Yes, since 0 falls in the confidence interval, there is sufficient evidence to indicate a difference in the two population means.Yes, since 0 falls in the confidence interval, there is insufficient evidence to indicate a difference in the two population means.    Yes, since 0 falls outside the confidence interval, there is sufficient evidence to indicate a difference in the two population means.No, since 0 falls in the confidence interval, there is sufficient evidence to indicate a difference in the two population means.No, since 0 falls outside the confidence interval, there is insufficient evidence to indicate a difference in the two population means.

Answer 1

a.)

The correct answer is a. Yes, we can say that its ok to use pooled standard deviation.

When the sample sizes are nearly equal , then a good Rule of Thumb to use is to see if this ratio of standard deviarion falls from 0.5 to 1.

In our case, S1/S2 = 0.9

Also, the ratio of variance is less than 3. So, we can use pooled standard deviation.

b.)

The observed value is given ins output as: 0.06

The P-Value for t-test is: 0.95

c.) Given Pooled standard deviation is: 4.42

So, Pooled Variance = square of pooled standard deviation = 4.42 * 4.42 = 19.53

d.)

Correct answer is part A.

Since p-value is greater than 0.10, there is not sufficient difference to indicate the difference in population means.

The results are not significant.

e.) 95% is given as:

(-4.9, 5.2)

f.)

-> If a 95% confidence interval includes the null(0) value, then there is no statistically meaningful or statistically significant difference between the groups.

-> If the confidence interval does not include the null(0) value, then we conclude that there is a statistically significant difference between the groups.

In our case the confidence interval (-4.9,5.2) contains NULL value.

So, we can say there is insufficient evidence to indicate the difference in 2 Population means.

Hence Part B is correct.

"Yes, since 0 falls in the confidence interval, there is insufficient evidence to indicate a difference in the two population means"

Also it supports our observations in question d