Question

Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election or coronation. Treat the values as simple random samples from larger populations. Use a 0.10 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation. Complete parts (a) and (b) below. All measurements are in years El Click the icon to view the table of longevities of archbishops and monarchs a. Use a 0.10 significance level, and test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs The test statistic isRound to two decimal places as needed.) The P-value is(Round to three decimal places as needed.)

Answer 1

a)

H0: mu1 = mu2

Ha: mu1 < mu2

x1(bar) = 13.25

x2(bar) = 16.33

s1 = 4.46

s2 = 2.46

n1 = 24

n2 = 12

SE = sqrt[ (s12/n1) + (s22/n2) ]

(s12/n1) = 0.8270

(s22/n2) = 0.5051

SE = 1.1541

df = 12 - 1 = 11 .. conservative approach

Test Statistics

t = [ (x1 - x2) - d ] / SE

t = -2.6715

p-value = 0.0109

As p-value is less than the significance level, we reject the null hypothesis.

Option A

b)

x1bar - x2bar = -3.08

SE = 1.1541

CI = 95%

DF = 11

t-value = 2.2010

ME = t*SE = 2.5402

Confidence Interval, (x1bar - x2bar) +/- ME

Lower bound = -5.62358

Upper bound = -0.54308

Confidence Interval (-5.6236 , -0.5431 )

Yes, because the confidence interval contains only negative values.