Question

A researcher comparing the means of dependent samples consisting of 30 matched pairs and obtained a mean difference of 5 and a standard error of the mean difference of 2. The confidence interval for the mean difference was (1.6, 8.4). What confidence level was used in constructing the interval

Answer 1

91.08%

Explanation:

Confidence interval = (1.6, 8.4)

Sample size (n) = 30

Standard Error (E) = 2

Mean (m) = 5

The confidence interval is obtained using the relation :

Mean ± Zcritical * standard error

5 ± Zcritical * 2

5 - (Zcritical * 2) = 1.6

5 - 2Zcritical = 1.6

5 - 1.6 = 2Zcritical

3.4 = 2Zcritical

Zcritical = 3.4 / 2

Zcritical = 1.7

From Z probability calculator

P(Z < 1.7) = 0.044565

α = 1 - (0.044565 * 2) = 0.91087

0.91087 * 100% = 91.08% = 91%

Hence, confidence level = 91.08%