Hypothesis Testing

I am not sure how to start this. Any help would be appreciated.

A random sample of 256 credit unions that offer credit cards revealed that the average annual fee charged by a credit union was $ 12.56 with a standard deviation of $2.33. A random sample of 225 federally chartered banks offering credit cards showed that the average annual fee was $16.48, with a standard deviation of $ 5.18. Because the samples are of significant size we may assume that the sample standard deviation is equal to the population standard deviation. Looking at the sample mean we are ready to make the claim that the difference in the annual fee charged by the banks is more than $3.00 more than that charged by the credit unions. The bank manager's association may want to reduce fees so they would like this tested at an alpha level of 0.05.

The alternate hypothesis is: ____
The null hypothesis is:____
The hypothesised difference in the population means is:____
This hypothesis test will be right/left/ or two tailed?
______________
The difference in the sample means is expressed by what combination of symbols? ____ The best estimation of the population VARIANCES is:
sigma-1 _______ and sigma-2 ______

Hi Brit

Hypothesis testing is the backbone of statistics. So, you're given two sets of data. One on credit unions and one on banks. First thing you do is list what you know.

Credit Union

\(\displaystyle n=256;\mu=12.56;\sigma=2.33\)

Banks

\(\displaystyle n=225;\mu=16.48;\sigma=5.18\)

Now, what's the claim? The claim is that the difference between the bank and credit union fee's are GREATER than 3. That's an inequality. Now, a rule of thumb is that the null hypothesis has an equivalency and the alternate hypothesis does not. In other words, the null hypothesis is either, \(\displaystyle =\) , \(\displaystyle \ge\), or \(\displaystyle \le\). Since the claim is GREATER than 3, that's the alternate hypothesis. The null hypothesis would then be the other option, and that other option (or what else it could be) is \(\displaystyle \le3\). You see now that there is an equivalency there.

Since it is an inequality and not an equality, it cannot be a two tailed test. Only an equality is two tailed. That is to say, if your claim is that one thing is equal to something else. When you use inequalities, it is either a left or right tailed test.