Hypothesis Tests Involving Two Sample Means or Proportions Formulas?

[renegade0865]

In this chapter of my book "Introduction to Business Statistics 7th Edition" we're learning about "Hypothesis Tests Involving Two Sample Means or Proportions" page 367 for me.

There is a page that gives us 3 formulas to use, but are vague on what circumstances to use them in.

Question 1:

To use pooled variance formula S^(2)(sub-P) I need to know whether population standard deviations are equal. Does the problem need to write out "assume population standard deviations are equal" or is there a way to know when a problem has equal population standard deviations to use "pooled variance formula S^(2)(sub-P)"? In my book the example and similar online examples don't write out "assume population standard deviations are equal", but they use the formula anyways. But, in my practice problems they always write out "assume population standard deviations are equal". So, I am very confused on when to use this.

Question 2:
When the population standard deviation are not equal I am allowed to use t-test and z-test. The t-test is for any sample size and z-test only if n1n2>30. In this case can I always just use t-test whenever population standard deviation are not equal and forgo the z-test? Is the z-test merely just a simpler method if n1n2>30?

My biggest concern is question 1, because the practice question in the book are very similar but slight change in wording requires different formulas.

 

[stapel]

...the practice question in the book are very similar but slight change in wording requires different formulas.

What formula do you think you should use? Why? (If you're right, volunteers can confirm. If you're wrong and we know what you're thinking, then volunteers can help clear up conceptual issues and get you back on track.)

Please be complete. Thank you!

 

[hincape_95]

hypothesis test to determine average income of males/female if different, equal varia

I was given this homework question to do and i am completely lost and confused. I need to know what my statistical decision would be and what my p-value would be. I'm not completely sure if I did it right.


At 5% significance level, conduct a hypothesis test to determine whether the average incomes of male and female employees are significantly different. (Assume equal variance).

State the null and alternative hypotheses:
The null hyptheses: There is no significant difference in the average income of male and female employees
The alternative hypotheses: There is a significant difference in the average income of male and female employees

Justify your choice of statistical method:
We will do a t-test sample size, two samples, because the sample size is less than 30.
My test is two-tailed because I am looking for the difference between the average income and male and female.

Find the critical value:
The T-Critical value for two-tail is 2.004879

Find the test value:
The T-Stat value is -0.09874

Make the statistical decision: (NOT SURE IF IT'S RIGHT)
Since the T-test value is not in the critical area, I do not have evidence to support the null hypothesis. The average income of male and female employees are significantly different


Find and interpret the p-value (NOT SURE IF IT'S RIGHT)

My p-value is very small 0.92171. This is much less than 5% so I have evidence to reject the null hypothesis.

0r

My p-value is 0.92171. This means I have a p-value of 27.1% chance of incurring an error when the null hypothesis is rejected. Since this is more than the allowable 5% significance level.