Question

A certain type of battery is said to last for 2000hours. A sample of 200 of these batteries were tested; the mean life was 1995 hours and the standard deviation of the lives was 25.5 hours. Use these data to test the hypothesis that the population mean life is 2000 hours against the alternative that it is less than 2000 hours. State the level of significance you are using in your test.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2000
Alternative Hypothesis, Ha: μ < 2000

Rejection Region
This is left tailed test, for α = 0.05 and df = 199
Critical value of t is -1.653.
Hence reject H0 if t < -1.653

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1995 - 2000)/(25.5/sqrt(200))
t = -2.773

P-value Approach
P-value = 0.003
As P-value < 0.05, reject the null hypothesis.

Here, we use 0.05 level of significance