Consider the following measurements of blood hemoglobinconcentrations (in g/dL) from three human populations at differentgeographic locations:

population1 = [ 14.7 , 15.22, 15.28, 16.58, 15.10 ]

population2 = [ 15.66, 15.91, 14.41, 14.73, 15.09]

population3 = [ 17.12, 16.42, 16.43, 17.33]

Perform ANOVA to check if any of these populations havedifferent mean hemoglobin concentrations. (Assume that all theANOVA requirements such as normality, equal variances and randomsamples are met.) After you perform ANOVA perform a Tukey-Kramerpost-hoc test at a significance level of 0.05 to see whichpopulations actually have different means. As usual, round allanswers to two digits after the decimal point. (Make sure you roundoff to at least three digits any intermediate results in order toobtain the required precision of the final answers.) For anyquestions, which ask about differences in means or test statistics,which depend on differences in means provide absolute values. Inother words if you get a negative value, multiply by -1 to make itpositive.

QUESTION 13

1. What is the standard error of the difference between the meansof population 2 and population 3, needed to calculate theTukey-Kramer q-statistic?  

QUESTION 14

1. What is the Tukey-Kramer q-statistic for populations 2 and 3?(Report the absolute value, if you get a negative number, multiplyby -1)

QUESTION 15

1. For the hemoglobin data of the three populations, what is thecritical value of the q-statistic required to reject the nullhypothesis of the Tukey-Kramer test at a significance level of0.05?

QUESTION 16

1. Which populations are have different means according to theresults of the Tukey-Kramer test? Select all that apply, you mayneed to select more than one correct answer to get credit for thisquestion.

   		Population 1 and Population 2
   		Population 1 and Population 3
   		Population 2 and Population 3
   		None of the above. All populations have the same means.