Question

ucccss in challenging calls. Campletc parts (a) trough (c) below H, p, #P2 Identfy the test stictic Round to two decimsl places ss needed.) Idently the P-value Pvalue Hound to thraa dacimal placea as neacad) What is the conclusion bated on the hypathesis test? The P-vslue i b. Test tha dlaim by constructing an apprapriata conidenca Intarval. the significanoe level ofa-0.05, so Th85% confidence intervel is- "(p1 p2) Rcund to threc decimal places as necded.) What is the conclusion based on the confidence interval? appaarto ha a signicantdiarance batwean tha ten propotions Thera ' | ค.idancs to warrant injection of thพิ daim that men and women have equalsinessa in challenging caBa c. Bused on the reults, dees t appear that men and women may have equal success in chalenging cals? Ο B. The confidence itoral suggests that thon匕נ 디gnhcant difference between te success of men and women n chalengng cals itis razonable to speculate that men have more success O C. The confidence interval augges thet there no signicant ciflerence between the succeas of men and women in chalenging cals O D. There is not enough information to reach a concluaion

Answer 1

Ho:   p1 - p2 =   0
Ha:   p1 - p2 ╪   0

first sample size,     n1=   1399
number of successes, sample 1 =     x1=   425
proportion success of sample 1 , p̂1=   x1/n1=   0.30378842
      
second sample size,     n2 =    752
number of successes, sample 2 =     x2 =    218
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.289893617
      
difference in sample proportions,    p̂1 - p̂2 =     0.013894803
      
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.29893073
      
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)   0.020699897
      
Z-statistic =    (p̂1 - p̂2)/SE =     0.67

p-value = 2*P(z>0.67) = 0.502

decision :    p-value>α,Don't reject null hypothesis   
p-value is greater than significance level,so, do not reject null hypothesis.there is not enough evidence…........

b)

Std error , SE =    SQRT(p̂1 * (1 - p̂1)/n1 + p̂2 * (1-p̂2)/n2) =     0.0206
Z critical value =   Z α/2 =    1.9600
      
margin of error , E =   Z*SE =    0.0404
      
confidence interval is       
lower limit =    (p̂1 - p̂2) - E =    -0.0265
upper limit =   (p̂1 - p̂2) + E =    0.0543

so, confidence interval is (-0.027,0.054)

because confidece interval limits contains 0, there does not appear to be a signficant…........there is not enogh evidence…..............

c)

option c)