9or 10 (0 complete) This Quiz: 10 pts possible In a fandom sample of males, it w
ID: 3313474 • Letter: 9
Question
9or 10 (0 complete) This Quiz: 10 pts possible In a fandom sample of males, it was found that 27 wite with their keft hands and 214 do not in a random sample of females, it was found that 71 wete with their le hands and 457 do not. Use a 0 05 sigcance level to test the claim ha the rate o lefi handedness among males is less than that aong lemales Complete parts (a) hrough (c) below a. Test the claim using a hypothesis test gio bethe sagle of males and the second sanple io be the sane ol lemaes Wate the nand atmativo hypotheses r e hypothesis test? a Libeary videos Round to two decimal places as needed) Cack to select your answers Type here 1o seanch 6tu 2 3 4 5Explanation / Answer
Solution:
a) F. H0: p1 = p2 H1: p1 < p2
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p1 = 27/(27+214) = 0.112033
p2 = 71/(71+457) = 0.134469
Z = (p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)
= (0.112033-0.134469)/sqrt(0.112033*(1-0.112033)/214+0.134469*(1-0.134469)/457)
= -0.84
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It is a left-tailed test.
So the p-value = P(Z<-0.84) = 0.20045(from standard normal table)
The P-value greater than in the significance level of ?=0.05
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so fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females.
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Given a=0.1, Z(0.05) = 1.645 (from standard normal table)
CI = (p1-p2) ± Z*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)
= (0.11203-0.134469) ± 1.645*sqrt(0.11203*(1-0.11203)/214+0.134469*(1-0.1344698)/457)
= (-0.0665, 0.0217)
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