assignment six Chegg Study l Guided Solutio × e Assignment Six Statistics And e
ID: 3324812 • Letter: A
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assignment six Chegg Study l Guided Solutio × e Assignment Six Statistics And e Statistics and Probability ques × Holly × c secure https://www.webassign.net/web/Student/AssignmentResponses/submit?dep#17334163 6. 0/1 points Previous Answers MendStat14 8.E.037 My Notes Ask Your A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A random sample of 500 registrations are selected from a Department of Motor Vehicles database, and 95 are classified as sports utility vehicles. (a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.) to (b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.) decrease Za/2 by decreasing the confidence coefficient increase the sample size n increase za/2 by increasing the confidence coefficient conduct a non-random sample decrease the sample size n Need Help? Read It Talk to a Tutor Submit Assignment Save Assignment Progress Home My Assignments Extension Request WebAssign 4.01997-2017 Advanced Instructional Systems, Inc. All rights reservedExplanation / Answer
6.
a.
TRADITIONAL METHOD
given that,
possibile chances (x)=95
sample size(n)=500
success rate ( p )= x/n = 0.19
I.
sample proportion = 0.19
standard error = Sqrt ( (0.19*0.81) /500) )
= 0.018
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 * 0.018
= 0.034
III.
CI = [ p ± margin of error ]
confidence interval = [0.19 ± 0.034]
= [ 0.156 , 0.224]
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DIRECT METHOD
given that,
possibile chances (x)=95
sample size(n)=500
success rate ( p )= x/n = 0.19
CI = confidence interval
confidence interval = [ 0.19 ± 1.96 * Sqrt ( (0.19*0.81) /500) ) ]
= [0.19 - 1.96 * Sqrt ( (0.19*0.81) /500) , 0.19 + 1.96 * Sqrt ( (0.19*0.81) /500) ]
= [0.156 , 0.224]
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interpretations:
1. We are 95% sure that the interval [ 0.156 , 0.224] 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
b.
Yes,
Estimate the proportion of sports vehicles in california with high degree of accuracy by increasing the sample size and as well as z /2
then the increasing the confidence interval because sample size is increasing means there from standard normal table, two tailed z /2 also increases.
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