Question

A survey asked. How many to do you can have on your body of the 1237 males surveyed, 10 responded that they had at least one tattoo oft 1094 females surveyed, 129 responded that they had at least one tattoo Constructa 90% confidence Weal to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of female that have at least one tattoo Interpret the interval Let P, represent the proportion of males with tattoos and p, represent the proportion of females with toos. Find the 90% confidence Herval for P- The lower bound The upper bounds (Round to three decimal places as needed) Interpret the interval O A. There is 90% 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 to OB. There is 90% 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 90% probabilly 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 90% probability that the ference of the proportion is in the interval Candude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tatoo

Answer 1

Confidence interval:

r₁ = number of success of population 1,

r₂ = number of success of population 2,

n₁ = sample size of population 1,

n₂ = sample size of population 2

= r₁ / n₁   = 189/ 1237 = 0.153

P1

= r₂ / n₂   = 129 / 1094= 0.118

* 1

F
= 1-
P1
= 1 – 0.153 = 0.847

92
= 1-
* 1
= 1- 0.118 = 0.882

n₁ = 1237

n ₂ = 1094

z_c = 1 -0.90 = 0.10/2 = 0.05

z_c = 1.645             Using standard normal table

z 100 101 102 103 104 105 106 07 1.08 109 0.0 5000 5040 15060 5120 160 519 529 529 5319 5359 0.1 5398 548 5478 5517 5557 5596 5636 5675 5714 5753 102 5793 5832 5871 5910 5948 5987.50 26 .5064 .6103 6141 0.35196217 6255 .623 6331 1.6368 6406 .5443 .6480 6517 0.4 6554 5591 .6628 .6664 6700 1.576 6.6808 .6844 6879 05 6915 .6950 .6985 .019 054 088 123 717 7190 .224 0.6 27 291 324 37 389 3422 44 486 57 59 0.7 580 611 1.7642 763T04 74 764 794 18237852 08 .881 910 99 1967 1995 8023 805] 8078 8106 818 09 819 8186 1.8212 828 8264 8289 8315 8340 18365 8389 11.0 8413 8438 1.8461 8485 8508 8531.8554 85元 1.859 18621 1.1 1.8643.8665 18686 8708 8729 1.8749 1.8TO 8790 18810 8830 1.2 .8849 8869 18888 89078925 1.8944 8962 .8980 8997 9015 139032 9049 9066 9082 9099 9115 9131 9147 9162 91 1.4 9192 9207 9222 9236 9251 9265 929 9292 19306 9319 15 9332 9345 9357 90 982 9394 9406 9418 19429 9441 19452 9463 9474 9484 19495 9505 9515 9525 955 9545 19554 9564 19573 9582 9591 9599 9608 9616 19625 9633

Using excel function "=NORMSINV(0.05)"

=NORMSINV(0.05) E D F -1.645 =NORMSINV(0.05) NORMSINV(probability)

Confidence Interval:

$(\hat{p_{1}}-\hat{p_{2}})\pm z*\sqrt{\frac{\hat{p_{1}}*\hat{q_{1}}}{n_{1}}+\frac{\hat{p_{2}}*\hat{q_{2}}}{n_{2}}}$

$= (0.153-0.118)-1.645*\sqrt{\frac{(0.153*0.847)}{1237}+\frac{(0.118*0.882)}{1094}}$

$= (0.153-0.118)+1.645*\sqrt{\frac{(0.153*0.847)}{1237}+\frac{(0.118*0.882)}{1094}}$

(0.153 -0.118) – 1.645 * 0.014132   and (0.153 -0.118) + 1.645 * 0.014132

0.021 <   (p₁ - p₂₎   < 0.049

As both limit having positive sign, That means there is 90% confidence that the proportion is in the interval, Conclude that there is a significant difference in the proportion of males and female that have at least one tattoo.