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Question

This Quiz: 2 pts possibl This Question: 1 pt Heip PIP Idenbily the test staleic dentity the oriical valueps) to theee decimal places as needed Use a comma to separate answers as needed) Whuat is the conckusion based on the hypothesitest? the null hypothesis There is evidence to conclude that pyP Round to three dedimal places as eeded) What is the condusien based on the conidence intervan the null hypothesis since the hypothesis test suggests thait p Activate Windows Click to select your answerls)

Explanation / Answer

PART A.
Given that,
sample one, x1 =22, n1 =40, p1= x1/n1=0.55
sample two, x2 =1290, n2 =1800, p2= x2/n2=0.717
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.55-0.717)/sqrt((0.713*0.287(1/40+1/1800))
zo =-2.305
| zo | =2.305
critical value
the value of |z | at los 0.01% is 2.576
we got |zo| =2.305 & | z | =2.576
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -2.3048 ) = 0.0212
hence value of p0.01 < 0.0212,here we do not reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: -2.305
critical value: -2.576 , 2.576
decision: do not reject Ho
p-value: 0.0212

PART B.
CI = (p1-p2) ± sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )
where,
p1, p2 = proportion of both sample observation
n1,n2 = size of both group
a = 1 - (confidence Level/100)
Za/2 = Z-table value
CI = confidence interval
CI = [ (0.55-0.7167) ± 2.58 * 0.0794]
= [ -0.3715 , 0.0381 ]
----------------------------
interpretations:
1) we are 99% sure that the interval [ -0.3715 , 0.0381] contains the difference between
true population proportion P1-P2
2) if a large number of samples are collected, and a confidence interval is created
for each sample, 99% of these intervals will contains the difference between
true population mean P1-P2

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