Data was collected between 1996 and 1998 on ear pierces and tattoos for male Pen
ID: 3387480 • Letter: D
Question
Data was collected between 1996 and 1998 on ear pierces and tattoos for male Penn State students. Assume these men represent a random sample of male Penn State students. The results were:
Tattoo?
Ear Pierce?
No
Yes
Total
No
381
43
424
Yes
99
42
141
Total
480
85
565
For both, give the desired interval and be sure to interpret the interval.
A) For the population of men without an ear piercing, find a 90% confidence interval for the proportion with a tattoo.
B) For the population of men with an ear piercing, find a 90% confidence interval for the proportion with a tattoo.
Ear Pierce?
No
Yes
Total
No
381
43
424
Yes
99
42
141
Total
480
85
565
Explanation / Answer
a)
Note that
p^ = point estimate of the population proportion = x / n = 43/424 = 0.101415094
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.014660471
Now, for the critical z,
alpha/2 = 0.05
Thus, z(alpha/2) = 1.644853627
Thus,
Margin of error = z(alpha/2)*sp = 0.024114329
lower bound = p^ - z(alpha/2) * sp = 0.077300765
upper bound = p^ + z(alpha/2) * sp = 0.125529424
Thus, the confidence interval is
( 0.077300765 , 0.125529424 ) [ANSWER]
*********************
b)
Note that
p^ = point estimate of the population proportion = x / n = 42/141 = 0.29787234
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.038513552
Now, for the critical z,
alpha/2 = 0.05
Thus, z(alpha/2) = 1.644853627
Thus,
Margin of error = z(alpha/2)*sp = 0.063349156
lower bound = p^ - z(alpha/2) * sp = 0.234523185
upper bound = p^ + z(alpha/2) * sp = 0.361221496
Thus, the confidence interval is
( 0.234523185 , 0.361221496 ) [ANSWER]
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