Question

A survey asked, "How many tattoos do you currently have on your body?" of the 1216 males surveyed, 197 responded that they had at least one tattoo. Of the 1009 females surveyed, 142 responded that they had at least one tattoo. Construct a 99% 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, represent the proportion of males with tattoos and P2 represent the proportion of females with tattoos. Find the 99% confidence interval for P1 - P2 The lower bound is The upper bound is (Round to three decimal places as needed.) Interpret the interval O A. There is 99% confidence that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo B. There is 99% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo OC. There is a 99% probability that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo OD. There is a 99% probability that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo

Answer 1

#1 ) Let x1 be the number of male respondent have at least one tattoo.

x2 be the number of female respondent have at least one tattoo.

Given :
Ir
= 197,
12
= 142,
11
= 1216 ,
2
= 1009 , $//img.homeworklib.com/questions/ce937870-e581-11ea-bb45-15be1cd27da3.png?x-oss-process=image/resize,w_560$₁ =
Ir
/
11
= 0.162, $//img.homeworklib.com/questions/cf6a2f50-e581-11ea-84ca-334ed3e619d1.png?x-oss-process=image/resize,w_560$₂=
12
/
2
= 0.1407 ,

$//img.homeworklib.com/questions/d04e4000-e581-11ea-8353-33d873c73d74.png?x-oss-process=image/resize,w_560$₁ = 1 – $//img.homeworklib.com/questions/d09a9a40-e581-11ea-a4d1-2d8975b79016.png?x-oss-process=image/resize,w_560$₁ = 0.8380 , $//img.homeworklib.com/questions/d0ebba20-e581-11ea-ac16-bdd0fc640e94.png?x-oss-process=image/resize,w_560$₂ = 1 – $//img.homeworklib.com/questions/d133af20-e581-11ea-ad6d-e1e4ee6727ca.png?x-oss-process=image/resize,w_560$₂ = 0.8593

confidence level = 0.99

Therefore α = 1 - 0.99 = 0.01 , 1 - (α/2) = 0.9950

So we have to find z score corresponding to area 0.9950 on z score table

So z = 2.575

99% confidence interval is given by :

(Pi - P2) + 2* P1 * q P2 * 92 + n1 n2

=

(0.1620 -0.1407)-2.575 * (0.162 +0.8380) 1216 - (0.1407 * 0.8593) 1009

( -0.018 , 0.060 )

Lower bound = -0.018

Upper bound = 0.060

The interval contain 0 , therefore ,

B. There is 99% confidence that the difference of the proportion is in the interval.Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.

#2)

Let R be red balls = 6 , O be orange balls = 7 and G be green balls = 8

Total balls = 21  

P( R or O ) =

Number of red balls + Number of Orange balls Total balls

= ( 6+7 ) / 21

Probability = 0.619

#3)

C. The probability 0.25 means that approximately 25 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 25 times since the probability refers to what is expected in the long-term, not short-term