STAT 2023, Assignment 18, Lesson 17, Comparing Two Population Means when the
population variances are not assumed equal.
Part One: Reading and Writing
Write a summary in your own words of at least four sentences of the following site down
to the section titled “Test Your Understanding.”
http://stattrek.com/estimation/difference-in-means.aspx?Tutorial=AP .
Part Two: Calculation
The average sales for two brands of external hard drives were compared using the following data.
Fifteen weeks of sales were recorded for each type of hard drive. Use this information to answer
the remaining questions.
Type One
n1=15
_
x1 = 456 units sold
s12 = 150
Type Two
n2=15
_
x2 = 426
s22 = 90
1. What is the point estimate for the mean sales of type one hard drive?
2. What is the estimated standard error for the point estimate for the mean sales of type one
hard drive? Round to two digits past the decimal.
3. What is the point estimate for the mean of sales for type two hard drive?
4. What is the estimated standard error for the point estimate for the mean of sales of type
two hard drive? Round to two digits past the decimal.
5. What is the value of the test statistic to test that the mean of population one is equal to
450? Round to one digit past the decimal.
6. What is the numerical value of the point estimate for the difference between the average
sales for these two types of hard drive?
7. What is the pooled variance estimate based on these two samples?
8. What is the degree of freedom associated with the pooled variance estimate above?
9. What is the estimated standard error for the point estimate for the difference between the
means, if the population variances are assumed equal?
10. What is the estimated standard error for the point estimate for the difference between the
means, if the population variances are not assumed equal? Is this equal to the answer
in the question just above? If so, why are these two equal?
11. What is the appropriate alternative hypothesis if the research question is “Do the data
indicate that the average sales for hard drive type one is more than the average sales for
hard drive type two?”
12. What is the numeric value of the test statistic that would be used to attempt to support the
alternative hypothesis described in the above question? Assume equal population
variances.
13. What is the appropriate alternative hypothesis if the research question is “Do the data
indicate that the average sales for hard drive type one is greater than 25 dollars more than
the average sales for hard drive type two?”
14. What is the numeric value of the test statistic that would be used to attempt to support the
alternative hypothesis described in the above question?
15. If the sales averages for the two hard drive types are equal, what is the name of the
distribution of the test statistic, if the standard error is based on the variance estimate that
is used when the population variances are assumed equal?
16. In this situation the null hypothesis would be rejected at the 1% significance level if the
observed test statistic value is more than what value?
17. If the p-value of this hypothesis test is 0.009 would one conclude that the average sales
for hard drive type one is more than the average sales for hard drive type two at the 5%
significance level? Answer with YES or NO.