Question

An engineer wants to know if the average amount of energy used in his factory per day has changed since last year. The factory used an average of 2,000 megawatt hours (mwh) per day prior to last year. Since last year, the engineer surveyed 400 days and found the average energy use was 2,040 mwh per day. Assume that the population standard deviation is 425 mwh per day.
a. Specify the null and alternative hypotheses to determine whether the factory's energy use has changed.
b. Calculate the value of the test statistic and the p-value.
c. At the 5% significance level, can you conclude that the energy usage has changed? Explain.

Answer 1

Answer:

The calculated value Z = 1.8823 <1.96 at 0.05 level of significance

The average amount of energy used in his factory per day has changed since last year.          

Step-by-step explanation:

Step(i):-

Given that mean of the Population = 2000 (MWH)

Given that size of the sample 'n' = 400

Given that mean of sample x⁻ = 2040 MWH

Given that the standard deviation = 425 MWH per day

Step(ii):-

Null hypothesis:H₀: μ = 2000 (MWH)

Alternative Hypothesis:H₁: μ≠ 2000( MWH)

Test statistic

                 $Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

                $Z = \frac{2040-2000}{\frac{425}{\sqrt{400} } }$

               Z =  1.8823

The calculated value Z = 1.8823 <1.96 at 0.05 level of significance

Final answer:-

The calculated value Z = 1.8823 <1.96 at 0.05 level of significance

The average amount of energy used in his factory per day has changed since last year.