## Hypothesis Testing and confidence interval questions

These are a few questions from my textbook and I am just unsure on my answers to the problems, any confirmation/help is greatly appreciated!

(Click on the image and it will lead to image shack and then click on the image again to enlarge it)

Q1.

I know that I and II are both true, however I am unsure on III. I think III is false as we CAN use the p value to test the mean is greater than 0. This is because a p value of 0.03 means that if the mean IS 0 then the probability of yielding a t statistic of less than -1.99 or greater than 1.99 is 0.03. This can then be used to compare with a significance level to decide whether or not we should reject the hypothesis that the mean is 0 or not reject it. What do you guys think?

Q2.

Consider a hypothesis test concerning the average marks in a subject called A with a null hypothesis that the mean mark is 60. Suppose we know the variance and use a significance level of 0.1 and that we calculate a test statistic of -1.5. Which of the following conclusions are correct?

I. There is evidence to suggest that the average mark in A is different to 60.

II. There is evidence to suggest that the average mark in A is greater than 60.

III. There is evidence to suggest that the average mark in A is less than 60.

a. II and III only
b. III only
c. I only
d. II only
e. None of the statements are correct

Now I picked e. This is because assuming we are using the students t distribution, we need to find a critical value given the significance level of 0.1. However to work out the critical value we need to know not only the significance level but also the degrees of freedom which depends on the size of the sample taken (which we don't know) so we can't calculate the critical value thus e.

Q3.

I picked a. as it is the only choice I know that is definitely true. However are any of the other options true? I don't really get what they mean...

Q4.

I picked c. This is because since the sample variance (and thus sample standard deviation) of the 2 samples are the same, this implies that their population counterparts of the 2 samples are also the same hence c. Not sure if I interpreted this question correctly at all :S

Thanks for any help!