ike\'s housemate Ally is trying to convince Mike to get a piercing. Mike is very
ID: 3321377 • Letter: I
Question
ike's housemate Ally is trying to convince Mike to get a piercing. Mike is very sensitive to popular opinion, and will only get one if "everyone else is doing it". Mike will get the piercing if Ally can show that more than 50% of students at Mike's college have one. Ally wastes no time in taking a random sample of 120 people from Mike's campus. Her sample of 120 revealed 72 people who admitted to having a piercing. Find a 95% confidence interval for the estimate of the population proportion of students that have a piercing. What is the margin of error for this confidence interval? Write a statement to interpret this confidence interval. Will Mike get the piercing? Why or why not? b. d.
Explanation / Answer
we knwo that the confidence interval of proportions is given as
p +- z*sqrt(p*(1-p)/n)
here p = 72/120 = 0.6
and the margin of error is
z*sqrt(p*(1-p)/n) , where z = 1.96
1.96*sqrt(0.6*(1-0.6)/120) = 0.087
so the 95% CI is
0.6+0.087 , 0.6-0.087
0..687, 0.513
c)
This means that we are 95% confident that the true value of the proportion would lie in the range
0.513, 0.687
d
as the confident interval is 51.3% to 68.7% , so the value is greater than 50% , so mike will get the piercing done
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