Answer to Question #178641 in Statistics and Probability for Allisha

Question

The following data represent the number of hours that a rechargeable battery operates before a recharge is required: 1.5, 2.2, 0.9, 1.3, 2.0, 1.6, 1.8, 1.5, 2.0, 1.2, 1.7. Use the sign test to test the hypothesis at 0.05 level of significance that the battery operates with an average of 1.8 hours before requiring a recharge. State clearly your assumptions.

Answer 1

H₀: No difference in average of the signed differences μ = 1.8

H₁: Median of the signed difference is less than zero μ ≠ 1.8

Total number of “+” value = 3

Total number of “-” value = 7

Test statistic:

Minimum of (3,7) = 3

x=3

Level of significance α=0.05

P-value = 2P (x≤3 when p=1/2)

$=2 \sum_{x=0}^{3}p(x;10, 1/2)$

= 2(0.001+0.010+0.044+0.117)

= 0.344

P-value>0.05

We do not reject the H₀.

The average operating time is not significantly different from 1.8 hours.