Question

a) Test the null hypothesis that the mean wage gap is 0 at the α = 0.01 level.

= = Exercise 10. (10 points) Hypothesis Testing A team of researchers is intersted in exploring the mean wage gap between male and female nurses, defined as gap MM - uF and collects data from two samples nM 91 and nF 121 obtaining the following information: XM = $26.32 XF = $27.21 SM = $20.11 s $18.27

b) If you constructed 95% and 99% confidence intervals for the mean wage gap, would those confidence intervals include 0?

Answer 1

XM - $26.32 XF = 27.21 M = 20.11 2 = 16:27 I AME M=91, nf= = 12 | hypothesis is Hoi An - UF - 0 VS Hi: Up - MF to 9) To gap is test null hypothesis that the mean woge o at the x=0.01 Level. test statistic is XM-X N NN(0,1) 2 sp ch + nm пF 26.32 - 27.21 20:1) gi + 18.27 121 =-1.4592 and critical rallel is 2212= 2000/2 = 20.005 2:58 hore 121 L Z212 hence Accept Ho CSScanned with CamScanner

(X17 - Xp) - 2012 b) :) To construct Construct 95% confidence interval of mean wage gap. here x = 0.05 The (1-x) 100 y. confidence interval is Si ((* SM nm + SI ,( Fmy - 7+) + Z_1215en is При пр. nF to constreeet 95% c. I hence = 0.05. 20U 27-21)- Z0005 (26.32 18.27 (26.32 - 27.21)+ Z0095 * + gi 1211 18.27 + 2011 gi 121 (-2.0854,0.3054) hence 95% confidence in terual is (-2.0854,0-3054) 99% C.I. :) How to find hero R=0:0) (14m-*) - 20.012 डल 2 F ( *pi-5p) + Z000122 Sa+s + SE NE nm som NE ((26.32 - 27-21 ) -2:58 2011. + 15:27 (26-32 - 27:21 )+ 2.58* 91 12) 200 gi + 18.27 121 c (-2:46 35, 0.6835) we seen that, 0 include both the interval. CSScanned with CamScanner