A study is done by a community group in two neighboring...

A study was conducted by a community group in two neighboring colleges to determine which one graduates students with more math classes. College A sampled 11 graduates. Their average was four math classes with a standard deviation of 1.5 math classes. College B sampled nine graduates. Their average was 3.5 math classes with a standard deviation of one math class. The community group believes that a student who graduates from college A has taken more math classes, on average. Both populations have a normal distribution. Test at a 1% significance level. Answer the following questions. Is this a test of two means or two proportions? Are the population standard deviations known or unknown? Which distribution do you use to perform the test? What is the random variable? What are the null and alternative hypotheses? Write the null and alternative hypotheses in words and in symbols. Is this test right, left, or two-tailed? What is the p-value? Do you reject or not reject the null hypothesis? At the ___ level of significance, from the sample data, there ______ (is/is not) sufficient evidence to conclude that ______.

Transcript

00:01 Hello, girls, so let's do the statistics problem, but before i get started, i recommend that you do the question of yourself.

00:06 I come back to see if you got it around or a lot.

00:11 So hopefully you've done it yourself now, so we're good it together.

00:13 So we have that a study is done by a community group and two neighboring colleges to determine which one graduates the students with more math classes, right? we have college a has 11 graduates average four math classes, standard division 1 .5, so we're given a bunch of data.

00:30 And we have the community group believes that a student graduates from college a has taken more math classes on average.

00:39 So we have that as our hypothesis or our claim rate.

00:44 So we're claiming that the community group believes that college a has taken more math classes on the average.

00:49 So both populations have a normal distribution.

00:52 We want to have a test at 1 % of the level of significance.

00:56 And our first part is asking us to complete the hypothesis test.

01:01 So the question is asking us if this test is a test of two means or two proportion.

01:09 Well, it's given in the question this test is a test of two means.

01:17 We're given two means in the question.

01:19 We're not given proportions or anything related to that way.

01:24 And that question is more about dyslogics.

01:26 So the second part is asking us if the population standard deviations are known or unknown.

01:31 And because this test is a test of two means and as normal distribution follows in normal distribution, we have that our population standard evasions are unknown.

01:42 We're given our sample standard deviations in the question if anyone is confused by that.

01:47 So the population are we have to complete the which distribution do we have to use.

02:03 So if we look at our sample size, we're given sample sizes that are less than 30, so they're considered to be small sizes.

02:14 So we would use a test.

02:16 If the sample sizes were greater than 30, then we would be considered large.

02:21 So we would just do a z test.

02:26 So this is a t test or t distribution with degrees of freedom.

02:34 18 so our degrees of freedom they look like n1 plus n2 minus 2 so that would be 11 graduates plus 9 graduates minus 2 which is 18 degrees of freedom so that's the part next we need to answer what the random variable is the random variable is going to be the variable that is the variable that we are experimenting or focusing on, which is the math classes, right? that's we're wanting to know the graduates and the college a &b and the math classes that they're taking.

03:16 So our random variable is going to be classes taken.

03:23 And then the next part is asking us what the null and alternative hypotheses is.

03:29 So our null hypothesis for our h0 is going to be the mua.

03:38 So our average for our college a equal to mu b.

03:44 So this aligns with the test b of two means, right? in the null hypothesis, it's always equal to.

03:53 So the muse are always equal to something, whether it be zero or another mu from another sample.

04:00 So in this case, the mues or the means are equal to the college a equal college b.

04:08 So that's going to be h .a.

04:13 So our alternative hypothesis is going to be mu a.

04:18 And now we have two options or three options more.

04:22 Like it could be mu a, the average of community or college a could be greater than less than or not equal to the average of college b...

Question

Please give Ace some feedback