Set # 8 1. (Text Problem 12.2) In a random sample of 20 males, the sample mean weight was 170 lbs. and the sample variance was 250 lbs# . (Note the unit of measurement for the sample variance: pounds squared. The sample standard deviation is measured in pounds. This is irrelevant to solving this problem--I just thought you would like to know). Find the prob-value for the hypotheses H! : . ")! @= H" : . ")! What would you conclude if, for this test, !&? 2. First, read the section \"Two-Sided Hypothesis Tests.\" Now consider a population with unknown mean . and unknown variance. In a random sample of size 50 we find \\ 23 and =# "& a. Find the 95% confidence interval for .. (you did this in PS #7). b. Test H! : . ## vs. H" : . ## at !& c. In a sentence or two, compare your results from parts a and b. 3. Consider a population with unknown mean . but known variance 5# 4. In a random sample of size 15 we find \\ 3 Test H! : . 4 vs. H" : . 4 at "! 4 First, read the section \"Hypothesis Tests for differences in Means\" (Text Problem 12.12). As a development economist, you are interested in whether individuals in country A have a lower mean income than those in country B. You have available independent random samples of size 50 each from the two populations. In these samples, \\ E $&!! \\ F $'!! =E $#!! =F $$!! Assuming the population variances are equal, find the prob-value and test the hypotheses L! : .F .E ! LE : .F .E ! 5. Recall that in random sampling from a normal population R . 5# the quantity 8=# 5# ;#8" Suppose I sample 8 "& from a normal population with unknown variance and find =# "( For the test H! : 5# "! vs. H" : 5# "!, find the exact prob-value (using =chidist in Excel), and bound the prob-value using the ;# table. 6. Suppose \\ is a discrete random variable given by \\ T \\ ! " #1 " "1 # $1 " for "$ 1 "# I wish to test L! 1 "# @= L" 1 "$, based on a single observation List all possible hypothesis tests and plot their characteristics