# Stat 2507 Assignment 4 U

MTB>random 9 c1-c20;SUBC>normal 68.71 3.MTB>tinterval 0.90 c1-c20a. How many of your intervals containμ? 17 (any number greater than 14 is acceptable.b.Would you expect all 20 of the intervals to containμ? [0.5]No. Why? Expected is(20)(0.90)=18 [1.5]c.Do all the intervals have the same width? No. Why (what is the theoretical width)?2(t0.05)s/√nwheresis changed from sample to sample. d. Suppose you took 95% intervals instead of 90%. Would they be narrower or wider?Widere. How many of your intervals contain the value 71? 6, but any number between 5 and16 is acceptable.f.Suppose you took samples of sizen= 64 instead ofn= 9. Would you expect more orfewer intervals to contain 71?  Fewer. What about 68.71? Same What about the widthof the intervals forn= 64: Would they be narrower or wider than forn= 9?  Narrower.3.Hypothesis testing forμwhenσis knownImaging choosingn= 16 women at random from a large population and measuring theirheights. Assume that the heights of the women in this population are normal withμ= 63.8inches andσ= 3 inches. Suppose you then test the null hypothesisH0:μ= 63.8 versus thealternative thatHa:μ6= 63.8, usingα= 0.10. Assumeσis known. Simulate the results ofdoing this test 30 times as follows:MTB>random 16 c1-c30;SUBC>normal 63.8 3.MTB>ztest 63.8 3 c1-c30a. In how many tests did you rejectH0. That is, how many times did you make an“incorrect decision”? I had 3 p-values less than 0.10, but any number≤8 is acceptable. 