Question

RIGHT CLICK ON THE IMAGE AND SELECT "OPEN IMAGE IN A NEW TAB" FOR A LARGER CLEARER IMAGE. WILL UPVOTE ANY HELP, THANKS

B Question Help A survey asked, "How many tattoos do you currently have on your body?" Of the 1249 males surveyed, 176 responded that they had at least one tattoo. Of the 1060 females surveyed, 129 responded that they had at least one tattoo. Construct a 90% 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 90% 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 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 OB. There is a 90% 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 OC. 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 tattoo OD. There is a 90% 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

Here, , n1 = 1249 , n2 = 1060
p1cap = 0.1409 , p2cap = 0.1217

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.1409 * (1-0.1409)/1249 + 0.1217*(1-0.1217)/1060)
SE = 0.0141

For 0.9 CI, z-value = 1.64
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.1409 - 0.1217 - 1.64*0.0141, 0.1409 - 0.1217 + 1.64*0.0141)
CI = (-0.004 , 0.042)

The lower bound is -0.004
The upper bound is 0.042

OPtion A) is correct interpretation