A random sample of 250 men yielded 175 who said they'd ridden a motorcycle at some time in their lives, while a similar sample of 215 women yielded only 43 that had done so. Find a 99% confidence interval for the difference between the proportions of men and women who have ridden motorcycles.
.4688 ± .085
.5 ± .112
.5 ± .103
.5 ± .085
.5 ± .078
.5 ± .103
Let's look at your data:
n1 = 250
n2 = 215
p1 = 175/250
p2 = 43/215
Formula:
CI99 = (p1 - p2) ± 2.58 √(p1(1-p1)/n1 + p2(1-p2)/n2)
Substitute the values into the formula and calculate. (Convert all fractions to decimals.)
You should be able to select your answer once you have determined the interval.
.5 �} .103, because, as the math guru said the formula is (p1 - p2) �} 2.58 �ã(p1(1-p1)/n1 + p2(1-p2)/n2), the 2.58 comes from the z-score table. The question doesn't want you to solve the whole formula, just the first and last.. (175/250)-(43/215)=.5 and the �ã(p1(1-p1)/n1 + p2(1-p2)/n2=.1026887336
Thank you. <3 @Math Whizz
To find the confidence interval for the difference between the proportions of men and women who have ridden motorcycles, we can use the formula:
CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
where:
- p1 and p2 are the proportions of men and women, respectively, who have ridden motorcycles
- Z is the critical value based on the desired confidence level (in this case, 99%)
- n1 and n2 are the sample sizes of men and women, respectively
First, we need to calculate the proportions of men and women who have ridden motorcycles:
p1 = 175 / 250 = 0.7
p2 = 43 / 215 ≈ 0.2
Then, we need to find the critical value, Z, corresponding to a 99% confidence level. Since we want to find a two-tailed interval, the remaining 1% of probability needs to be divided equally between the two tails. This leaves 0.5% on each tail, giving us an alpha value of 0.005.
Using a Z-table or Z-calculator, we can find that the critical value for a 99% confidence level is approximately 2.576.
Now, we can plug in all the values into the formula:
CI = (0.7 - 0.2) ± 2.576 * sqrt((0.7 * (1 - 0.7) / 250) + (0.2 * (1 - 0.2) / 215))
CI = 0.5 ± 2.576 * sqrt((0.7 * 0.3 / 250) + (0.2 * 0.8 / 215))
Calculating the expression inside the square root:
sqrt((0.7 * 0.3 / 250) + (0.2 * 0.8 / 215)) ≈ 0.085
Finally, we substitute this value into the confidence interval formula:
CI = 0.5 ± 2.576 * 0.085
The correct answer is therefore:
CI = 0.5 ± 0.219
So, the 99% confidence interval for the difference between the proportions of men and women who have ridden motorcycles is approximately:
0.5 ± 0.219
Hence, the correct option is .5 ± .219.