SOLUTION: Do you pay for certain web services? Georgia Institute of Technology's Graphics visualization and usability center surveyed 13,000 internet users and asked them about their willing

Question 297586: Do you pay for certain web services? Georgia Institute of Technology's Graphics visualization and usability center surveyed 13,000 internet users and asked them about their willingness to pay fees for access to web sites. of these 2,938 were definitely not willing to pay such fees.
a) at the 0.06 level of significance, and assuming that the 13,000 users were randomly selected, test the claim that more than 75% of internet users are willing to pay fees for access to web sites.
b) assume the 13,000 users were randomly selected. Construct a 95% interval for the proportion definitely unwilling to pay fees.
C) determine the minimum sample size necessary if you want to be 95% confident that the sample percentage of internet users who are unwilling to pay fees has a margin of error of two percentage points. assume that you have no prior knowledge of the percentage of internet users who are unwilling to pay fees.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Georgia Institute of Technology's Graphics visualization and usability center surveyed 13,000 internet users and asked them about their willingness to pay fees for access to web sites. of these 2,938 were definitely not willing to pay such fees.
a) at the 0.06 level of significance, and assuming that the 13,000 users were randomly selected, test the claim that more than 75% of internet users are willing to pay fees for access to web sites.
Ho: p <= 0.75
Ha: p > 0.75 (claim)
Critical Value: invNorm(0.94) = 1.5548
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Test Stat: z(10062/13000) = (0.774-0.75)/sqrt[0.75*0.25/13000] = 6.3195
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p(value) = P(z>6.3195) = normalcdf(6.3195,100) = 0.000000000132..
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Since the test stat is in the reject interval, reject Ho.
--
The test results support the claim.
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b) assume the 13,000 users were randomly selected. Construct a 95% interval for the proportion definitely unwilling to pay fees.
sample proportion: 0.774
standard error: 1.96*sqrt[0.75*0.25/13000] = 0.007
95% CI: 0.774-0.007 < p < 0.774+0.007
or 0.767 < p <0.781
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C) determine the minimum sample size necessary if you want to be 95% confident that the sample percentage of internet users who are unwilling to pay fees has a margin of error of two percentage points. assume that you have no prior knowledge of the percentage of internet users who are unwilling to pay fees.
---
n = [z/E]^2(pq)
---
n = [1.96/0.02]^2(0.5*0.5)
---
n = [2401]
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Cheers,
Stan H.
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