2. A wind farm off the cost of Scotland consists of 60 wind turbines, each expected...

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2. A wind farm off the cost of Scotland consists of 60 wind turbines, each expected to generate 3 MW of electrical energy when the wind speed is between 15-25 m/s (at gale strength), with a standard deviation of 0.4 m/s depending on other weather conditions. When the wind speed exceeds 25 m/s the turbines are switched off to minimise damage to the blades. In the following days, engineers conduct an investigation to assess if any of the wind turbines have been damaged and whether the farm's energy output has been reduced. Following Storm Isha, the engineers found that the average energy generated from the 60 turbines on the next day when the winds where at gale strength was 2.87 MW. Conduct an appropriate hypothesis test at the 1% significance level to investigate whether the expected amount of generated electricity from a farm's turbines is unaffected or has been impacted by Storm Isha. Clearly state your hypotheses, all definitions and any assumptions you have made in your investigation. If the expected energy output from the turbines has been reduced to 2.87 MW, then what is the power of your hypothesis test? 2. A wind farm off the cost of Scotland consists of 60 wind turbines, each expected to generate 3 MW of electrical energy when the wind speed is between 15-25 m/s (at gale strength), with a standard deviation of 0.4 m/s depending on other weather conditions. When the wind speed exceeds 25 m/s the turbines are switched off to minimise damage to the blades. In the following days, engineers conduct an investigation to assess if any of the wind turbines have been damaged and whether the farm's energy output has been reduced. Following Storm Isha, the engineers found that the average energy generated from the 60 turbines on the next day when the winds where at gale strength was 2.87 MW. Conduct an appropriate hypothesis test at the 1% significance level to investigate whether the expected amount of generated electricity from a farm's turbines is unaffected or has been impacted by Storm Isha. Clearly state your hypotheses, all definitions and any assumptions you have made in your investigation. If the expected energy output from the turbines has been reduced to 2.87 MW, then what is the power of your hypothesis test?