Question

The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. A random sample of 15 devices is selected and found to have an average life of 5625.1 hours and a sample standard deviation of 226.1 hours.

Required:
a. Construct and interpret a 95% (two sided) confidence interval for the population standard deviation of the life of a biomedical device.
b. Test the hypothesis that the true mean life of a biomedical device is greater than 5500 using the P-value approach.

Answer 1

Part a [5522.3511 ; 5727.8488]

Part b. The p-value is 0.050115.

The H0 is rejected and concluded that the true mean life of a biomedical device is greater than 5500.

Explanation:

The 95 % confidence interval for the mean of the population is given by

∝= 1- 0.95= 0.05

υ= n-1= 15-1= 14

x`± t ∝() s / √n

5625.1 ± { t (0.05) (14)} 226.1 / √15

5625.1 ± 1.76 * 226.1/3.8729

5625.1 ± 102.7488

[5522.3511 ; 5727.8488]

Part b

State the null and the alternate hypothesis

H0: u= 5500 against the claim Ha: u > 5500

the test statistic

t= x`- u/ s/ √n

t= 5625.1-5500/226.1 / √15

t=2.143

The p-value is 0.050115.

The result is not significant at p < 0.05.

The H0 is rejected and concluded that the true mean life of a biomedical device is greater than 5500.