Hypothesis testing???

I am in so much trouble on this...I have looked at so many examples and I still do not know what to do.
Can someone please help me with this problem?

Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with σ = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces):

Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?

1. State the hypothesis you will test.

1. Calculate the test statistic.

1. Find the P-value.

1. What is the conclusion?

I don't know whether to use t or z or what...I started out trying to do it with t, but then it seemed like I didn't have enough information. I just don't understand...

Well, the problem says "Because of the small sample size, the t distribution will be used" so I cannot see why you would be wondering about that.

The "t" distribution is \(\displaystyle z\sqrt{n- 1}\) where z is the standard normal distribution. What did you get for z and t?

HallsofIvy said:

Well, the problem says "Because of the small sample size, the t distribution will be used" so I cannot see why you would be wondering about that.

The "t" distribution is \(\displaystyle z\sqrt{n- 1}\) where z is the standard normal distribution. What did you get for z and t?

Click to expand...

Oops, I added that as a note to myself when I started working the problem. It wasn't in there initially.

First I calculated the mean and got 5.989, then .12 for the sample standard deviation.
For t, I subtracted 6 from 5.989 and then divided .12/sqr10 to get -.2902. 9 degrees of freedom. That is all I have...why would I have to find t and z? I don't even know how to look t up on the t table because I have no clue what percent to use...that is why I thought maybe I am doing something wrong and should be using just z since I don't think you need a confidence interval or percent error thing or whatever (yeah, I am also clueless about that stuff at this point).