Question

Context: The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with standard deviation of 20 hours. A random sample of 15 thermo- couples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. Is there evidence to support the claim that mean life exceeds 540 hours? Use Minitab for the computations for this problem. The data set is on Canvas. Copy/paste your Minitab output as part of your work. One-Sample Z: EX4-42 Descriptive Statistics N 15 Mean StDev SE Mean 95% CI for u 551.33 14.81 5 .16 (541.21, 561.45) u mean of EX4-42 Known standard deviation = 20 Test Null hypothesis Ho: u = 551.33 Alternative hypothesis Hiu 551.33 Z-Value P-Value 0.00 0.999 Conduct the 5-step process for the hypothesis test. Use a = 0.05.

Answer 1

answer)

Null hypothesis Ho : u = 540

Alternate hypothesis Ha : u < 540

As the population s.d is known here we can use standard normal z table to conduct the test

Test statistics z = (sample mean - claimed mean )/(s.d/√n)

From minitab output

Sample mean = 551.33

N = 15

Claimed mean = 540

S.d = 20

After substitution

Z = (551.33 - 540)/(20/√15) = 2.19

From z table, p(z<2.19) = 0.9857

As the obtained p-value is greater than given significance level

We fail to reject Ho

So we do not have enough evidence to conclude that mean life exceed 540 hours