Homework. Chapter 11 Homework core: 0 of 1 pt 1.1.29 Given below are the number
ID: 3319402 • Letter: H
Question
Homework. Chapter 11 Homework core: 0 of 1 pt 1.1.29 Given below are the number of successes and sample size for a simple random sample from a population 3of19(o complete) ! x = 16, n= 20, 99% level a. Determine the sample proportion b. Decide whether using the one-proportion z-interval procedure is appropriate c. If appropriate, use the one-proportion z-interval procedure to find the confidence interval at the specified confidence level d. If appropriate, find the margin of error for the estimate of p and express the confidence interval in terms of the sample proportion and the margin of error a. Type an integer or a decimal. Do not round) Clear All Enter your answer in the answer box and then click Check AnswerExplanation / Answer
11.1.29.
a.
possibile chances (x)=16
sample size(n)=20
sample proportion ( p )= x/n = 0.8
b.
yes, it is appropriate
Z test for proportion is used
c.
TRADITIONAL METHOD
given that,
possibile chances (x)=16
sample size(n)=20
success rate ( p )= x/n = 0.8
I.
sample proportion = 0.8
standard error = Sqrt ( (0.8*0.2) /20) )
= 0.089
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.576
margin of error = 2.576 * 0.089
= 0.23
III.
CI = [ p ± margin of error ]
confidence interval = [0.8 ± 0.23]
= [ 0.57 , 1.03]
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DIRECT METHOD
given that,
possibile chances (x)=16
sample size(n)=20
success rate ( p )= x/n = 0.8
CI = confidence interval
confidence interval = [ 0.8 ± 2.576 * Sqrt ( (0.8*0.2) /20) ) ]
= [0.8 - 2.576 * Sqrt ( (0.8*0.2) /20) , 0.8 + 2.576 * Sqrt ( (0.8*0.2) /20) ]
= [0.57 , 1.03]
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interpretations:
1. We are 99% sure that the interval [ 0.57 , 1.03] contains the true population proportion
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 true population proportion
d.
confidence interval = [ 0.57 , 1.03]
margin of error = 0.23
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