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 = …