A survey? asked, "How many tattoos do you currently have on your? body?" Of the
12281228
males? surveyed,
199199
responded that they had at least one tattoo. Of the
10701070
females? surveyed,
126126
responded that they had at least one tattoo. Construct a
9090?%
confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.Let
p 1p1
represent the proportion of males with tattoos and
p 2p2
represent the proportion of females with tattoos. Find the
9090?%
confidence interval for
p 1 minus p 2p1?p2.
The lower bound is
nothing.
The upper bound is
nothing.
?(Round to three decimal places as? needed.)
Interpret the interval.
A.
There is
9090?%
confidence that the difference of the proportions is in the interval. Conclude that there is
insufficient evidence of ainsufficient evidence of a
significant difference in the proportion of males and females that have at least one tattoo.
B.
There is a
9090?%
probability that the difference of the proportions is in the interval. Conclude that there is
aa
significant difference in the proportion of males and females that have at least one tattoo.
C.
There is
9090?%
confidence that the difference of the proportions is in the interval. Conclude that there is
aa
significant difference in the proportion of males and females that have at least one tattoo.
D.
There is a
90?%
probability that the difference of the proportions is in the interval. Conclude that there is
insufficient evidence of ainsufficient evidence of a
significant difference in the proportion of males and females that have at least one tattoo.
Sol:
Z crit for 90%=1.645
p1^=x1/n1=199/1228=0.1620521
p2^=x2/n2=126/1070=0.117757
90% confidence interval for diff in proportions
=p1^-p2^+-z crit*sqrt(p1^(1-p1^)/n1+p2^(1-p2^)/n2)
=0.1620521-0.117757+-1.645sqrt(0.1620521*(1-0.1620521)/1228+0.117757*(1-0.117757)/1070)
=0.0442951-0.02370587,0.0442951+0.02370587
=0.02058923,0.06800097
lower limit=0.021
upper limit=0.068
mark option C.
There is
9090?%
confidence that the difference of the proportions is in the interval. Conclude that there is
aa
significant difference in the proportion of males and females that have at least one tattoo.
Get Answers For Free
Most questions answered within 1 hours.