How to define variables and extrapolate information from the word problem
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How to define variables and extrapolate information from the word problem

[From: ] [author: ] [Date: 12-02-02] [Hit: ]
f) Value of Test Statistic for sample:First, calculate the pooled common variance since we are assuming both are coming from the same population. This formula will come right out of your textbook:variance = [(18-1)(114.16^2) + (12-1)(97.23^2)] / [(18-1) + (12-1)] = 11627std. dev.......

Sorry, can't do graphing in Yahoo Answers.

Degrees of freedom = N1 + N2 - 2 = 18 + 12 - 2 = 28 d.f.

0.02 significance with 0.01 in each tail of the distribution since H1 is "NOT EQUAL"

So, critical regions are values greater than 0.01 or less than -0.01

e) Critical Values: t = 2.467 (from t-table using 28 d.f. and alpha equal to 0.02 two tail test.


f) Value of Test Statistic for sample:

First, calculate the "pooled" common variance since we are assuming both are coming from the same population. This formula will come right out of your textbook:

variance = [(18-1)(114.16^2) + (12-1)(97.23^2)] / [(18-1) + (12-1)] = 11627
std. dev. = sqrt(variance) = sqrt(11627) = 107.83

Now, the standard error equals:

(std. dev.) (sqrt (1/18 + 1/12) ] = 107.83 (.3727) = 40.18

Finally, we can calculate the t-statistic:

t-statistic = (538.82 - 525.23) / 40.18 = 0.388

You can look up this t-statistic in a t-table to find the p-value:

p-value = 0.738 which is significantly greater than 0.02/2 = 0.01. The p-value is NOT in the critical region.

g) Statistical Conclusion:

Since t-statistic is less than the critical value: 0.388 < 2.467, DO NOT REJECT the null hypothesis

h) Sentence/Headline/Non-technical Conclusion in WORDS:

Based upon the data, the means for women and men are not significantly different.

Hope that helped
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