Question

The mean of the times (in minutes) it takes a lab technician to perform a certain task is of interest. The lab technician was observed on 5 different occasions and 14.5, 14.2, 14.4, 14.3 and 14,6 were recorded.
a) Assume that data are random sample from a normal distribution with variance 0.02.

b)Can we conclude that true mean time to perform this task is different than 14 minutes? Let α = 0.05. Calculate P-Value of the test.

Answer 1

Sample size = n = 5

Sample mean = = 14.4

Variance = 0.02

Population standard deviation = = 0.1414

Claim: True mean time to perform this task is different than 14 minutes.

The null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is known so we have to use z-test statistic.

Test statistic is

P-value = 2*P(Z > 6.33) = 0.0000

P-value < 0.05 we reject the null hypothesis.

Conclusion:

True mean time to perform this task is different than 14 minutes.