Developing a Statistic Test: Can I Have Some Help?

[brad sue]

Hi,
I have this problem that I cannot figure out what to do:

Given mean 1 =mu 1, variance =sigma1^2.
mean 2=mu2, variance =sigma2^2
Test hypothesis Ho: mu1=2*mu2 versus
H1: mu1>2*mu2.

Develop a statistic test.

Can I have some help?

 

[EnumaElish]

This is an odd problem. Typically the mean is a parameter, as opposed to a statistic. The two means are either equal or not. The statement "test hypothesis H0: 1=2 vs. H1: 1>2" does not make logical sense. I guess you have to assume the means are unknown and are estimated from the data. If so, you can apply the two sample t-test.

 

[tacman]

Sure, I'd be happy to help you develop a statistic test for this hypothesis. First, we need to determine what type of test we will use. Since we are comparing two means, a t-test would be appropriate in this situation.

Next, we need to calculate the test statistic. In this case, we will use the formula for the t-test for independent samples:

t = (x̄1 - x̄2) / √(s1^2/n1 + s2^2/n2)

Where x̄1 and x̄2 are the sample means, s1^2 and s2^2 are the sample variances, and n1 and n2 are the sample sizes for groups 1 and 2, respectively.

We will also need to calculate the degrees of freedom for the t-test, which is equal to (n1 + n2 - 2).

Once we have our test statistic, we can compare it to the critical value from a t-distribution table to determine if it falls in the rejection region, which would lead us to reject the null hypothesis and accept the alternative hypothesis.

I hope this helps you get started on developing your statistic test. If you have any further questions, please let me know. Good luck!