Use the information on the hypothesis test detailed below to determine which of the following statements is correct. Assume that the population from which the sample was drawn is normally distributed. Ho:u=25 Ha:u does not equal 25 Sample Size 20 Sample Mean 24 Sample Standard Deviation 9 Significance Level 5% Which of the following statements is most accurate? a. The null hypothesis should be rejected because 25 falls outside the acceptance range. b. The null hypothesis should be rejected because 25 falls within the acceptance range. c. The acceptance range is 19.8 to 28.2. d. The acceptance range is 20.8 to 29.2. Here is how Stalla says to solve it: 1. Compute Standard Error 9/square root of 20= 2.0125 2. Compute reliability factor =t.025, 19=2.093 3. 25+or-2.093(2.0125)=20.79 to 29.21 so the answer is letter D Where I get stuck is on part 2. computing the reliability factor. I think .025 is .05/2 which you get from the confidence interval and the 19 is 20(sample size) -1. What I want to know is, is there any other way other than using the table to come up with 2.093? I took the test in June and can not remember the CFA providing us with tables? Maybe I am over analyzing. Any thoughts or help would be appreciated. Thanks, Jason Here is my question or thought process please tell me if I am correct: 1. Identify the test statistic so:

Of course there are ways of coming up with the 2.093. There is a very simple series expansion described by Amos (1964) which uses a recursive relationship between confluent hypergeometric functions. Indeed, most statistical software implements this or various modifications of it. Or you could just use the tables they will provide for you on the problem.

>There is a very simple series expansion described by Amos (1964) which uses a >recursive relationship between confluent hypergeometric functions. Indeed, most >statistical software implements this or various modifications of it. I thought statistical tables were ancient wisdom handed down through oral tradition? You know, like logarithm tables and slide rules…

I, um, actually made it through high school with a slide rule.

Can someone please explain to me why we use U and not the sample mean when calculate the CI in this question? When I look through the schweser notes and other sourse, it seems to me that the formula for CI contains X which in this case is 24 and not U. Thanks!!!

i second masynya. I think the correct answer to this is C

I don’t know what an “acceptance range” is and it’s not some standard statistical term. However, one way that people teach hypothesis testing is to say that when you do a two-sided test (as above), you can calculate a C.I. X-bar ± [blah] and if the parameter value in H0 falls in that C.I. you fail to reject H0 and if it falls outside you reject H0 (I personally find this approach to hypothesis testing distasteful). What Stalla is doing is using the fact that “X-bar in mu ± [blah]” is equivalent to “mu in X-bar ± [blah]” (where “equivalent” means if first is true, second is true, etc) and then introducing something they call the acceptance region. Edit: “reliability factor” is also not a standard statistical term in hypothesis testing. This is some home-baked approach to hypothesis testing that leads nowhere good.

Thanks for the explanations JoeyDVivre ! I think what you said makes sense! It is kind weird to calculate CI using U. What we do need, however, is to estimate Z or t and depending on their values either support or reject null hypothesis.

yep.