This is not a HW problem. For the purpose of trading stock options, I am trying to learn statistics on my own.

A stock is currently selling at $50 . The terms of a call option specify that the stock will raise to $70 in 18 weeks. That is, the stock is expected to increase about 2%/week.

(1) To assess the reasonableness of the 2%, I would perform a t test for testing a hypothesized mean. Am I right?

(2) If the t test shows that the average historical growth rate is 2.1%, I would be able to calculate the 95% probability that the average historical growth rate of 2.1% is equal to or higher than 2.1%. Or, equal to or higher than 2%. That is, 2.1% and 2.0% are the hypothesized means. Am I right?

(3) How far back should I go (# of historical observations)? Can the sample size be calculated by performing a “power test”? How do I do it?

(4) Is there a test better than the t test?

Thank you!

Doctor T