Wednesday, September 22, 2010

Practice problems for homework 4

Here is a sample of pulse rates for females.

100, 97, 90, 88, 83, 82, 80, 80, 78, 77, 73, 72, 70, 69, 68, 67, 67, 60, 60, 60

1) Find n, x-bar, sx and the median.

2) Is -0.5 < z(median) < 0.5?

3) is proportion(z(high)) - proportion(z(low)) > 88%?

4) If yes to both question 2) and question 3), Find the 95% confidence interval for mux, where the endpoints are rounded to one place after the decimal point.

5) Find the 95% confidence interval for sigmax.

Answers in the comments.

1 comment:

Prof. Hubbard said...

100, 97, 90, 88, 83, 82, 80, 80, 78, 77, 73, 72, 70, 69, 68, 67, 67, 60, 60, 60

1) Find n, x-bar, sx and the median.

n = 20.

x-bar = 76.1

s_x = 11.7

median = 75


2) Is -0.5 < z(median) < 0.5?


(75-76.1)/11.7 = -.09, so okay.


3) is proportion(z(high)) - proportion(z(low)) > 88%?

z(100) = (100-76.1)/11.7 = 2.04
z(60) = (60-76.1)/11.7 = -1.38

2.04 corresponds to .9793
-1.38 corresponds to .0838

.9793 - .0838 = .8955, so okay.


4) If yes to both question 2) and question 3), Find the 95% confidence interval for mux, where the endpoints are rounded to one place after the decimal point.


n = 20, so df = 19 and CLM_95% = 2.093

76.1 - 2.093*11.7/sqrt(20) = 70.6
76.1 + 2.093*11.7/sqrt(20) = 81.6

70.6 < mu_x < 81.6 is the 95% confidence interval.



5) Find the 95% confidence interval for sigma_x.


chi square left = 8.907
chi square right = 32.852

11.7*sqrt(19/8.907) = 17.1
11.7*sqrt(19/32.852) = 8.9

8.9 < sigma_x < 17.1 is the 95% confidence interval.