# Null Hypothesis

• Jun 19th 2009, 03:52 AM
klore717
Null Hypothesis
I am new to statistics, I have the Megastat, but I don't think I am using it correctly. Any help would be greatly appreciated.

The production manager at Bellevue Steele, a wheelchair manufacturer, want to compare the number of defective wheelchairs produced on the day shift with the number on the afternoon shift. A sample of the production from 6 day shifts and 8 afternoon shifts revealed the following defects.

Day 5,8,7,6,9,7
Afternoon 8,10,7,11,9,12,14,9

at the .05 significance level, is there a difference in the mean number of defects per shift?

a. State the null hypothesis and the alternate
b. what is the decision rule
c. what is the value of the test statistic
d. what is the decision regarding the null hypothesis
e. what is the p-value
f. interpret the results
g. what are the assumptions necessary with this test.
• Jun 19th 2009, 07:15 AM
matheagle
you need to assume that the two samples are coming from normal populations.
Next we can either do this assuming the two population variances are equal
or that they are unequal, see...
Unequal sample sizes, unequal variance at Student's t-test - Wikipedia, the free encyclopedia

$H_0:\mu_1=\mu_2$ vs. $H_0:\mu_1\ne\mu_2$

IF we assume equal variances the test stat is

${\bar X_1-\bar X_2\over S_p\sqrt{{1\over n_1}+{1\over n_2}}}$

that has a t distribution with $n_1+ n_2 -2$ degrees of freedom.
(We can do a $\chi^2$ test to see if the pop variances are equal.)

If they are unequal, you need to do satterwaithe's approximation.

${\bar X_1-\bar X_2\over \sqrt{{S_1^2\over n_1}+{S_2^2\over n_2}}}$