ef more than Round to three decimal places as needed.) b) What is he confidence

Question

ef more than Round to three decimal places as needed.) b) What is he confidence interval for eountry A? Select the comeot choice below and, if necessary,fil in the answer boes within your choioe. Round to one decimal place as needed ) O B. The conditions for constructing a conidence interval are not satiofied Compare to the confidence interval for country B. Choose the correct anseer beow O B. E appears that the proportion of adults who feel tis way in country A is about the same as hose in couny B O C. tappears that the proportion of adults whe feel this way in country B is more than hose in couney A O D. tappears that the proportion of aduts who feel thiebaay in country A is more han those in country B MacBook Ai 5 2

Explanation / Answer

a.
given that,
sample one, x1 =1113, n1 =1555, p1= x1/n1=0.716
sample two, x2 =580, n2 =1292, p2= x2/n2=0.449
sample proportions of country A is more than country B
b.
TRADITIONAL METHOD
given that,
possibile chances (x)=1113
sample size(n)=1555
success rate ( p )= x/n = 0.7
I.
sample proportion = 0.7
standard error = Sqrt ( (0.7*0.3) /1555) )
= 0
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0
= 0
III.
CI = [ p ± margin of error ]
confidence interval = [0.7 ± 0]
= [ 0.7 , 0.7]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
possibile chances (x)=1113
sample size(n)=1555
success rate ( p )= x/n = 0.7
CI = confidence interval
confidence interval = [ 0.7 ± 1.96 * Sqrt ( (0.7*0.3) /1555) ) ]
= [0.7 - 1.96 * Sqrt ( (0.7*0.3) /1555) , 0.7 + 1.96 * Sqrt ( (0.7*0.3) /1555) ]
= [0.7 , 0.7] = (70%,70%)
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 95% sure that the interval [ 0.7 , 0.7] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion

TRADITIONAL METHOD
given that,
possibile chances (x)=580
sample size(n)=1292
success rate ( p )= x/n = 0.4
I.
sample proportion = 0.4
standard error = Sqrt ( (0.4*0.6) /1292) )
= 0
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0
= 0
III.
CI = [ p ± margin of error ]
confidence interval = [0.4 ± 0]
= [ 0.4 , 0.5]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
possibile chances (x)=580
sample size(n)=1292
success rate ( p )= x/n = 0.4
CI = confidence interval
confidence interval = [ 0.4 ± 1.96 * Sqrt ( (0.4*0.6) /1292) ) ]
= [0.4 - 1.96 * Sqrt ( (0.4*0.6) /1292) , 0.4 + 1.96 * Sqrt ( (0.4*0.6) /1292) ]
= [0.4 , 0.5] =(40%,50%)
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 95% sure that the interval [ 0.4 , 0.5] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion

compare both country A and B then confidence interval for A country is more than country B

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