Set #10 Hypothesis Testing Due in class: Tuesday, 4/12/16 1. Write a short paragraph on how you decide which of two competing hypotheses you would make the null hypothesis, H! , and which you would make the alternative hypothesis, H" . 2a. For the example done in class deriving and " for all the possible tests, redo the probability calculations for H ! : 1 6 vs. H" : 1 2 That is, fill in the entries in the table below: Let \\ F # : H! : .6 vs. H1 : : .2 8 " Test " # $ % & ' ( ) V 2 ! " # ! " ! # " # ! " # Vw ! " # # " ! # ! " # " ! 2 T VlL! ! " T V w lL" " " ! Hint: The easiest way to do this is to use the binomial probability function in Excel. Note that T VlL! could be written T Vl1 ' and, in particular for test (5) T \\ !l1 ' T \\ "l1 ' b. Plot the eight points in a graph similar to the one I sketched in lecture. Then indicate which tests are inadmissable (that is, which tests are above the envelope). 3. Given \\ R . "*. You have a sample of size 8 %% observations from which you find B '#. Test at !& the null hypothesis L! : . & @= L" . & a. Choose a test statistic. In this case, this is done for you, choose B. (What theorem or lemma in statistics leads us to the best choice, B, or test statistic in this case? b. Find - such that T B 5 - l.& !#& (why .025 and not .05?) c. Check if B & c, or if B & c. In either case, one would reject H! since this is a two-tailed test. Report your conclusion. 4. Suppose wages are normally distributed with an unknown mean and known standard deviation of $22/hour. From a sample of 120 wage earners you calculate an average wage of $38/hour. Test the null hypothesis that the population mean wage is 40/hour, against the alternative that it is less than $40/hour, at !" 5. Problem 12.4, page 256. Extra credit: In a simple random sample of 36 families you find the sample mean income B $9500 and the sample standard deviation = $2500. Test at !"! L! . $*!!! @= L" . $9000