A survey? asked, \"How many tattoos do you currently have on your? body?\" Of th

Question

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.

Explanation / Answer

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.

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