# Math Help - Test Statistics / Confidence Intervals - Lost : need a bit of help please

1. ## Test Statistics / Confidence Intervals - Lost : need a bit of help please

a)
Problem 4: Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to no sound at all. She randomly divides sixteen students into two groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Assuming equal population variance, do the data provide sufficient evidence to indicate that the mean scores differ between two groups with a 0.1 significance level? Their scores follow. For the constant sound group: 5, 9, 3, 7, 5, 6, 9, 8. And for the no sound group: 6, 4, 5, 3, 10, 6, 5, 3. A. Assume that the standard deviations are equal and find the test statistic for the test that the between mu1 and mu2 is zero.

b)
Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to no sound at all. She randomly divides sixteen students into two groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Assuming equal population variance, do the data provide sufficient evidence to indicate that the mean scores differ between two groups with a 0.1 significance level? Their scores follow. For the constant sound group: 6, 3, 10, 9, 4, 5, 1, 6. And for the no sound group: 8, 3, 6, 4, 5, 3, 2, 7. A. Assume that the standard deviations are equal and find the upper limit of the appropriate confidence interval for the difference between mu1 and mu2.

c)
Problem 1 (population proportions): In a survey conducted by Wright State University , senior high school students were if they had ever used marijuana. We are interested in whether there is a difference in use by male and female students. If 460 out of 934 male, and 463 out of 997 female students reported that they have tired marijuana, find the lower bound on a 99% confidence interval for the difference in the population proportions.

d)
Problem 2: In a survey conducted by Wright State University , senior high school students were if they had ever used marijuana. We are interested in whether there is a difference in use by male and female students. If 387 out of 1,138 male, and 376 out of 996 female students reported that they have tired marijuana, find the z-test statistic that you would use to test whether H0: p1 = p2.

Can someone show me how to do some of these? I'm so completely lost.

2. Originally Posted by jpd750
a)
Problem 4: Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to no sound at all. She randomly divides sixteen students into two groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Assuming equal population variance, do the data provide sufficient evidence to indicate that the mean scores differ between two groups with a 0.1 significance level? Their scores follow. For the constant sound group: 5, 9, 3, 7, 5, 6, 9, 8. And for the no sound group: 6, 4, 5, 3, 10, 6, 5, 3. A. Assume that the standard deviations are equal and find the test statistic for the test that the between mu1 and mu2 is zero.

The confidence interval for this is $\displaystyle (\bar{x_1}-\bar{x_2})\pm t_{(\frac{0.1}{2},n_1+n_2-2)}\times s\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$

What do you get?

3. ## a question 4

Seems to me you are looking at a straightforward between-subjects t-test, with an alpha level of .01
You need to compute the difference between the two sample means and divide by the estimated standard error. As with other versions of standard error this is Sum of Squared divided by Degrees of Freedom, except that in this case you have two SS and two DF, so you need to pool the variance, i.e. (SS for sample 1 + SS for sample 2) divided by (DF for sample 1 + DF for sample 2). For the calculation you can forget about mu - mu, as under the null hypothesis this always sums to zero.
Hope this helps, if you need further please feel free to reply. I'm new to this site so feel free to send me a personal email if that's easiest.