Here’s another one which confused me again… In the process of forecasting dividends for companies on the Nikkei Index, a senior portfolio manager claims that the current average dividend per share for stocks on the index is $2.50 per share (after currency conversion). A junior analyst on the team becomes concerned that it might not be good enough that the dividend simply equals $2.50 per share; in fact, he believes that in order to substantiate current dividend projections the average must be at least $2.50 per share. Accordingly, the junior analyst takes a sample of 15 Nikkei companies. This sample has a mean of $2.40 with a standard deviation of $0.25. Assuming the population is normally distributed, what is the calculated value of the test statistic and is the mean dividend at least $2.50 per share at the 5% level of significance? Shouldn’t it be: H0: ux<2.5 (H0 is what you want to reject) Ha: ux>=2.5 (Ha is what you believe) However is anwer is: H0: ux>=2.5 Ha:ux<2.5 Am I wrong on this one? I thought I was clear about these concepts but now I’m more confused than ever after doing these passmaster problems…

You’re wrong. The null hypothesis ALWAYS involves a form of equality (=, <=, >=), the alternate will have only , or “not equal”.

Well, what about H0: ux<=2.5 (H0 is what you want to reject) Ha: ux>2.5 (Ha is what you believe) ? and that didn’t convince me that the other way around is correct.

you’re not looking for at most 2.5, you’re looking for at least 2.5 or more but it atleast has to be 2.5. So considering the equality has to be in the null H0 it makes sense to say Ux is greater than or equal to 2.5.

so, what do we put for H0 and Ha? Is the following correct? H0: what you want to reject Ha: what you believe I’m totally confused by this h0 and ha thing.

it doesn’t matter, it’s whatever the signs work out 2 be. I know this is totally confusing u lol. If it says atleast 2.5 then by default that has to be the Null. So you might be looking for or believe the Ha or the H0, it doesn’t matter, you just have to set up the signs. Does that make sense at all?

Thank you JP. So for this one, it’s because of the = sign that we have to put ux>=2.5 into H0…

Fkcfa, if it states atleast or equal to “X” than you take it as the null, if not it’s forced to be the alternative. Sorry, lightly off the topic… I’ve seem to have fogotten the rules…would we be able to use the z-scores here? because its normally distributed and has a known stdev, even though the sample is less than 30? and lastly, will they provided the students t distribution?

Thank you Reineir, that was clear enough for me. We have to use t-score for this one cuz it’s normally distributed and the population variance is unknown, and also the number is <30. t critical is not provided in the question and we have to look it up in the book, which I hate a lot.

fkcfa, “So for this one, it’s because of the = sign that we have to put ux>=2.5 into H0…” That’s correct. Anything with the = sign <= or >= has to be assigned to H0 then just work from there Sorry it took so long to get back to u

Thank you for getting back to me! Glad that I asked the question here… It doesn’t confuse me any more!