SOLUTION: 1. A sample of 65 observations select from a somewhat normal population gave a mean of 2.67 with standard deviation of 0.75. A sample of 50 observations was independently taken f

Question 1206223: 1. A sample of 65 observations select from a somewhat normal population gave a mean of 2.67 with standard deviation of 0.75.
A sample of 50 observations was independently taken from normal distribution and the mean was 2.59 with standard deviation of 0.66
A. If the objective is to make a comparison of the mean of the two populations, which method is
appropriate and why?
B. Test whether the first population has greater mean as compared to the second. What is your conclusion at 5% level of significance?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample 1 has 65 observations with a mean of 2.67 and a standard deviation of .75.
sample 2 has 50 observations with a mean of 2.59 and a standard deviation of .66.

it looks like a two sample t-test would be appropriate for this.

test is to see if sample 1 mean is greater than sample 2 mean.
level of significance is .05.
it is one tail with the level of significant on the right side of the confidence interval.

i used the two sample t-test calculator at https://www.statskingdom.com/140MeanT2eq.html

inputs and results of the analysis are shown below.

inuts:

results:

at .05 right tail level of significance, critical t-score with 113 degrees of freedom would be equal to 1.66.

right tail critical p-value is .05.

the test t-score was .597
the test p-value was .2758

since the test t-score was less than the critical t-score, the results were not significant.
likewise, since the test p-value was greater than the critical p-value, the results were not significant.
these results are always consistent with each other, i.e. both significant or both not significant conclusions.

the graph shows that the test t-score are clearly within the confidence interval.

the conclusion is that there is not sufficient information to conclude that the first population mean was greater than the second population mean.
the population means are considered to be the same with differences due to normally expected variation in sample means.

the two sample t-test was used instead of the two sample z-test because the standard deviations were taken fom the samples and not from the population.

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