When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, an _ in appropriate?

When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, a t-test is appropriate.

To add, The analysis of two populations means through the use of statistical examination is called a t-test. Small sample sizes commonly use a t-test with two samples.  What statisticians call as test statistics are identified as t-values. A systematized value that is calculated from sample data during a hypothesis test is called a test statistic. The procedure that calculates the test statistic compares your data to what is expected under the null hypothesis.

You already have an experience with the basic principles behind a t-test if you’ve tried to communicated with a distracted teenager.

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.