1) Many states are carefully considering steps that would help them collect sale
ID: 3180356 • Letter: 1
Question
1) Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet? Assume that we want to be 95% confident that the sample percentage is within sevenseven percentage points of the true population percentage for all sales transactions.
n=?
2)
Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: four percentage points; confidence level 90% from a prior study, is estimated by the decimal equivalent of 56%
n=?
3)
Use the sample data and confidence level given below to complete parts (a) through (d).
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll,
n=970 and x=534
who said "yes." Use a 90% confidence level.
Click the icon to view a table of z scores.
a) Find the best point estimate of the population proportion p.
(Round to three decimal places as needed.)
b) Identify the value of the margin of error E.
Eequals=
(Round to four decimal places as needed.)
c) Construct the confidence interval.
Explanation / Answer
Q1.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.5
ME = 0.07
n = ( 1.96 / 0.07 )^2 * 0.5*0.5
= 196 ~ 196
Q2.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.645
Sample Proportion = 0.56
ME = 0.04
n = ( 1.645 / 0.04 )^2 * 0.56*0.44
= 416.728 ~ 417
Q3.
Q3.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=534
Sample Size(n)=970
Sample proportion = x/n =0.551
Confidence Interval = [ 0.551 ±Z a/2 ( Sqrt ( 0.551*0.449) /970)]
= [ 0.551 - 1.645* Sqrt(0) , 0.551 + 1.65* Sqrt(0) ]
= [ 0.525,0.577]
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