Question

An engineer wants to know if the average amount of energy used in his factory per day has changed since 2015. The factory used an average of 2000 megawatt hours (mwh) per day in 2015. Since 2015, the engineer surveyed 300 days and found the average energy use was 2040 mwh per day with a sample standard deviation of 400 mwh per day. (round your answers to four decimal places)

part a: Specify the null and alternative hypotheses to determine whether the factory's energy differs from its 2015 value.

part b: Calculate and report the value of the test statistic

part c: Calculate and report the p-value. At the 5% significance level, can you conclude using the p-value approach that the energy usage has changed? Explain.

part d: At the 5% significance level calculate and report the critical value(s). Can you conclude, using the critical value approach, that the energy usage has changed? Explain.

Answer 1

a)

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

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2040 - 2000)/(400/sqrt(300))
t = 1.7321

c)

P-value Approach
P-value = 0.0843
As P-value >= 0.05, fail to reject null hypothesis.

d)

Rejection Region
This is two tailed test, for α = 0.05 and df = 299
Critical value of t are -1.968 and 1.968.
Hence reject H0 if t < -1.968 or t > 1.968

As the value of test statistic, t is not within critical value range, fail to reject the null hypothesis