A drone manufacturer is evaluating the performance of two experimental battery designs, 'Volt-A' and 'Volt-B', to determine which provides superior endurance. Independent samples of each battery type were tested under identical load conditions, and the flight duration (in minutes) was recorded for each. The results are summarized in the table below:
| Battery Type | Sample Mean (xˉ\bar{x}xˉ) | Standard Deviation (sss) | Sample Size (nnn) |
|---|---|---|---|
| Volt-A | 24.8 | 3.2 | 50 |
| Volt-B | 23.1 | 4.1 | 65 |
By stating your hypotheses clearly, carry out a suitable test to determine whether there is evidence that the mean flight duration of the Volt-A battery is greater than that of the Volt-B battery. Use a 1% level of significance and state your test statistic and critical value.
The manufacturing cost for the batch of 50 Volt-A batteries was £450.00. The manufacturing cost for the batch of 65 Volt-B batteries was £390.00. The drone service generates a revenue of £1.50 per minute of flight endurance.
Using your results from part (a) and the cost data provided, advise the manufacturer on which battery type to select for production to maximize the expected profit per battery. Justify your answer.
