Statistics Problems Assignment
a. A confidence interval on the difference between means is computed using the following formula:
Lower Limit = M1 - M2 -(tCL)()
Upper Limit = M1 - M2 +(tCL)()
estimated standard error of the difference between means ()
MSE = (237.16 + 357.21)/2 = 297.185
Since n is 100,
= = 2.438
To calculate tCL, we need to know the degrees of freedom
Degrees of freedom = (n1 - 1) + (n2 - 1) = 198
From t table, it can be found that the t for a 95% confidence interval for 198 df is 1.972.
M1 - M2 = 131.4 – 120. 2 = 11.2
Lower limit = 11.2 – (1.972) (2.438) = 6.39
Upper limit = 11.2 + (1.972) (2.438) = 16.01
6.39 ≤ μ1 – μ2 ≤ 16.01
b. 1) The difference between the two sample proportions is 0.22 – 0.14 = 0.08
2) Standard error for difference
1. = 0.0414
2. = 0.347
3. ≈ 0.04
3) Difference Between the Sample Proportions ± z * (Standard Error for Difference)
0.08 ± (1.972) (0.04) or 0.08 ± 0.079
6. a. Percentage of people with successful treatment
73/ 125= 0.584
confidence level is 95%, so z value is 1.96
standard error for proportion
0.039
Lower limit = 0.584 - 1.96 * 0.039
Upper limit = 0.584 + 1.96 * 0.039
b. 0. 584 – 0.352 = 0.232
confidence level is 95%, so z value is 1.96
The formula for the estimated standard error is:
= 0.0575
Lower limit = 0.232 – 1.96 * 0.0575
Upper limit = 0.232 + 1.96 * 0.0575
8. a. standard error of the mean
5.1 / 10 = 0.51
Lower limit = 46.1 – 1.96 * 0.51
Upper limit = 46.1 + 1.96 * 0.51
b. 1) estimated standard error of the difference between means ()
MSE = (26.01 + 18.49) / 2 = 22.25
= = 0.67
2) 47.2- 46.1 = 1. 1
3) Lower limit = 1.1 – 1.96 * 0.67
Upper limit = 1.1 + 1.96 * 0.67
10. 1) 12/50 = 0.24
2) If CI = 90%, z value is 1.645
3) Standard error for proportion
0.006
4) Lower limit = 0.24 – 1.645 * 0.06
Upper limit = 0.24 + 1.645 * 0.06
13. a. 1) estimated standard error of the difference between means ()
MSE = (22.09 + 26.01) / 2 = 24.05
= = 0.69
2) 32.8 – 31.9 = 0.9
3) Lower limit = 0.9 – 1.96 * 0.69
Upper limit = 0.9 + 1.96 * 0.69
b. 0.54 – 0.48 = 0.06
confidence level is 95%, so z value is 1.96
The formula for the estimated standard error is:
= 0.07
Lower limit = 0.06 – 1.96 * 0.07
Upper limit = 0.06 + 1.96 * 0.07
c. 1) 0.4 – 0.38 = 0.02
2) confidence level is 95%, so z value is 1.96
3) The formula for the estimated standard error is:
= 0.069
4) Lower limit = 0.02 – 0.069 * 1.96
Upper limit = 0.02 + 0.069 * 1.96
15. Mean = 14.75, Standard deviation = …
