Question

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As part of its eco-friendly campaign, a company has asked for your advice whether installing a wind turbine will generate enough electricity to be cost effective. To produce enough electricity, the average wind speed needs to be least 12 mph. Based on historical data from the past 5 years, 41 days were randomly chosen and their wind speed measurements were written down. This resulted in an average wind speed of 15 mph with a standard error of 0.6872 mph. A histogram of these wind speeds yielded a right-skewed shape.

(a) Are the conditions met for constructing a confidence interval? (Check all that apply.)

It is reasonable to assume that weather conditions on the various days were independent of each other.The Nearly Normal condition is met.None of the conditions are met.The days were randomly chosen.

(b) Find the 98% confidence interval for the true average wind speed. (Use 4 decimal places)
(  ,  )

(c) Does the above confidence interval provide evidence that a wind turbine would be cost effective?

Yes, since the lower boundary is greater than the required wind speed of 12 mph, there is evidence the true average wind speed is greater than 12 mph.No, since the lower boundary is greater than the required wind speed of 12 mph, there is evidence the true average wind speed is greater than 12 mph.    No, since the lower boundary is less than the required wind speed of 12 mph, it is possible the true average wind speed is less than 12 mph.Yes, since the lower boundary is less than the required wind speed of 12 mph, it is possible the true average wind speed is less than 12 mph.

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As part of its eco-friendly campaign, a company has asked for your advice whether installing a wind turbine will generate enough electricity to be cost effective. To produce enough electricity, the average wind speed needs to be least 12 mph. Based on historical data from the past 5 years, 41 days were randomly chosen and their wind speed measurements were written down. This resulted in an average wind speed of 15 mph with a standard error of 0.6872 mph. A histogram of these wind speeds yielded a right-skewed shape.

(a) Are the conditions met for constructing a confidence interval? (Check all that apply.)

It is reasonable to assume that weather conditions on the various days were independent of each other.The Nearly Normal condition is met.None of the conditions are met.The days were randomly chosen.

(b) Find the 98% confidence interval for the true average wind speed. (Use 4 decimal places)
(  ,  )

(c) Does the above confidence interval provide evidence that a wind turbine would be cost effective?

Yes, since the lower boundary is greater than the required wind speed of 12 mph, there is evidence the true average wind speed is greater than 12 mph.No, since the lower boundary is greater than the required wind speed of 12 mph, there is evidence the true average wind speed is greater than 12 mph.    No, since the lower boundary is less than the required wind speed of 12 mph, it is possible the true average wind speed is less than 12 mph.Yes, since the lower boundary is less than the required wind speed of 12 mph, it is possible the true average wind speed is less than 12 mph.

Answer 1

(a) Conditions that are met:

It is reasonable to assume that weather conditions on the various days were independent of each other.

The Nearly Normal condition is met.

The days were randomly chosen.

(b) 98% Confidence interval :

At α = 0.02 and df = n-1 = 40, two tailed critical value, t-crit = T.INV.2T(0.02, 40) = 2.423

Lower Bound = x̅ - t-crit*se = 15 - 2.423 * 0.6872 = 13.3347

Upper Bound = x̅ + t-crit*se = 15 + 2.423 * 0.6872 = 16.6653

13.3347 < µ < 16.6653

(c) Yes, since the lower boundary is greater than the required wind speed of 12 mph, there is evidence the true average wind speed is greater than 12 mph.