STATISTICS

Statistics



Statistics

Problem 7.4

Data

n = 100

X = 10.6

S = 2.8

CI = 95 %

Solution

Standard error

=

S

=

2.8

=

2.8

=

0.28

v n

v 100

10

a = 1 - (C I / 100) = 0.05

Critical probability = 1 - 0.05/ 2 = 0.95/ 2 = 0.475

df = n - 1 = 100 - 1 = 99

the cumulative probability is equals to 0.475.

critical value = - 0.063.

ME = standard error * CV = 0.28 * - 0.063 = - 0.01764

Thus, for the 95 % CI, the population mean is in the range of 10.6 + - 0.01764.

10.58236 < µ > 10.61764

Problem 7.6

Data

n = 100

X = 3.38

S = 0.30

CI = 99 %

Solution

S E

=

S

=

0.3

=

0.3

=

0.03

v n

v 100

10

a = 1 - (C I / 100) = 0.01

Critical probability = 1 - 0.01/ 2 = 0.995

df = n - 1 = 100 - 1 = 99

the cumulative probability is equals to 0.995.

critical value = 2.626.

Margin of error = standard error * critical value = 0.03 * 2.626 = 0.07878

Thus, for the 95 % CI, the population mean is in the range of 3.38 + 0.07878.

3.45878 < µ > 3.30122

Problem 7.8

Data

n = 100

exactly 10

CI = 95 %

Solution

p =

10

=

0.1

100

v 0.1(1 - 0.1)/ 100 = v 0.09 / 100 = v 0.0009 = v 0.03

The 90 % CI estimate is 0.1 ± 2 (0.03), which is 0.16 to 0.04

Problem 7.12

Data

n = 100

53 patients at least once

CI = 95 %

Solution

p =

53

=

0.53

100

v0.53(1-0.53)/100 = v0.249/100 = v0.249/100 = v0.002491 = 0.05

The 95% CI estimate is 0.53 ± 2 (0.05), which is 0.629819838 to 0.430180162

Problem 7.16

Great Britain:

p =

528

=

0.51

1041

v 0.51(1 - 0.51)/ 1041 = v 0.2499/ 1041 = v 0.2499/ 1041 = v 0.00024 = 0.015

The 95 % CI estimate is 0.51 ± 2 (0.15), which is 0.81 to 0.21

Japan:

p =

311

=

0.28

1096

v 0.28 (1 - 0.28)/ 1096= v 0.2016/ 1096 = v 0.000184 = 0.0134

The 95 % CI estimate is ...