Question

5. The battery pack of a hand calculator is designed to perform at least 20,000 calculations before needing recharging. A new quality-control manager hired by the manufacturer is concerned that the pack may not be working for as long as the specification states. A sample of 114 packs resulted in an average of 19,695 calculations with estimated population standard deviation of 1,103.The quality-control manager concluded that her concerns are indeed confirmed by these data. At 10% level of significance, do you agree with the manager’s conclusion? Does your conclusion change at 1% level of significance? Please show your steps and explain your conclusion in each case. Also explain the difference between the two tests.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 20000
Alternative Hypothesis, Ha: μ < 20000

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (19695 - 20000)/(1103/sqrt(114))
t = -2.952

P-value Approach
P-value = 0.0019

As P-value < 0.1, reject the null hypothesis.

There is sufficient evidence to conclude that the mean is less than 20000
Test 2:
As P-value < 0.01, reject the null hypothesis.

conclusion do not change for 1% of significance