If two samples a and b had the same mean and standard deviation, but sample a had a larger sample size, which sample would have the wider 95% confidence interval? sample a as it comes first sample b as its sample is more dispersed sample a as it has the larger sample sample b as it has the smaller sample

Explanation:

Recall that the margin of error (MOE) is defined as

MOE = z*s/sqrt(n)

The sample size n is located in the denominator, meaning that as n gets bigger, the MOE gets smaller. The same happens in reverse: as n gets smaller, the MOE gets bigger.

Put another way, a small sample size means we have more error because small samples mean they are less representative of the population at large. The bigger a sample is, the better estimate we will have of the parameter.

We are told that "sample A had a larger sample size" indicating that sample A has a more narrow confidence interval.

Therefore, sample B would have a wider confidence interval.

This is true regardless of what the confidence level is set at.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

answer is 67%

step-by-step explanation: