The median annual income of subscribers to Shutterbug magazine is $75,000 (Home
ID: 3428210 • Letter: T
Question
The median annual income of subscribers to Shutterbug magazine is $75,000 (Home Theater website, August 18, 2008). A sample of 300 subscribers to Popular Photography & Imaging magazine found 165 subscribers with an annual income over $75,000 and 135 with an annual income under $75,000. Can you conclude that the median annual income of Popular Photography & Imaging subscribers differs from the median annual income of Shutterbug subscribers?
a.) What is the mean and standard deviation of the normal distribution that can be used for this statistical test (to 4 decimals if necessary)?
mean =______
Standard deviation= _______
b.) What is the value of the test statistic (to 2 decimals)?
________
________
Explanation / Answer
a)mean =300/2 =150
Standard deviation=sqrt(p*(1-p)/n)
=sqrt(0.5*0.5/300)
=0.0289
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(b)so, test statistic is
Z=(phat-p)/sqrt(p*(1-p)/n)
=(165/300-0.5)/sqrt(0.5*0.5/300)
=1.73
It is a two-tailed test.
So the p-value= 2*P(Z>1.73) =0.0836 (from standard normal table)
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