Gloria brown cfa calculated the intricinsic value of RTN company and expencts the stick to generate a 20% annual return over the foreseeable future. However, Brown is converned that her price forecast may be too high. She conducted a hypothesis test and colncluded at at 5% sig level, the null hypothesis can be rejected that RTN company’s invesmtne return would be equal to or less than 25% per year. The one tailed test utilised a z test. INdicate the meaining of the significance level chosen by brown and state the correct rejection region: brown will reject a true null hypothesis 5% of the time - which is fine I understand however with regards to the rejection region is it z > 1.645 or z < 1.645?
> 1.645. Think of the bell curve. Null hypothesis is that z is less than or equal to 1.645 std. deviations above the mean. Reject the null if the z score is greater than that.
that’s correct but the null hypothesis is that the company’s investment return would be equal to or less than than 25%. So surely it should be less than <1.645 as a rejection region? I know i’m wrong but not too sure why.
- She expects the return to be 20%. 2) She believes this estimate is too high. 3) She sets H0: mean annual return <= 25%, Ha: mean annual return > 25% 4) Since she was able to reject the null, then the mean return is probably more than 25%. She is dead wrong on her assumption that the estimate of 20% is too high. Her analysis showed that the return is even more than that! The rejection region is of course > 1.645. If you get a z value > 1.645 then the population mean is probably more than 25%, with a 5% probability of being wrong.
Again, picture the bell curve (graph of the density function of z). Draw the curve, make the center 0, draw a line at 1.645. Shade the region to the left of it. This is the null. The z score has to be greater than 1.645 (to the right of the shaded region) in order to provide significant evidence for you to know that the true underlying parameter does not lie in the shaded region.
wyantjs, what about the use of 25% instead of 20% in this problem?
We may want to make sure that wasn’t a typo first. My guess is that was supposed to be 20, not 25.