An aerospace firm compares the energy efficiency of two experimental propulsion configurations: Alpha and Beta. Data is recorded from a random sample of 45 missions for Configuration Alpha and a random sample of 50 missions for Configuration Beta. The findings for the energy consumption (in kWh per mission) are summarized below:
| Configuration | Sample Size (nnn) | Mean Energy Consumption (xˉ\bar{x}xˉ) | Standard Deviation (sss) |
|---|---|---|---|
| Alpha | 45 | 82.4 | 3.2 |
| Beta | 50 | 80.8 | 3.8 |
Stating your hypotheses clearly, test, at the 5% level of significance, whether there is evidence of a difference in the mean energy consumption between the two propulsion configurations.
Subsequently, an independent laboratory conducts a separate review of flight logs. Although Configuration Alpha consumed more energy on average in this review as well, the calculated test statistic for the difference in means was found to be z=1.58z = 1.58z=1.58.
An engineer claims that Configuration Alpha has, on average, a higher energy consumption than Configuration Beta.
Test the engineer's claim using the test statistic from the laboratory review (z=1.58z = 1.58z=1.58), stating the hypotheses and the critical value you would use. Use a 5% level of significance.