Question

the following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of 20 hurricanes that originated over the Atlantic Ocean in the last decade. A table of summary statistics for this data (as calculated in Homework 9) is also provided below.

In Homework 9, we determined the equation of the least-squares regression line:

and also calculated the estimated standard error of the model:

Use the information given above to complete the following statements. Perform each calculation using a single step in your calculator, and report your answers rounded to 3 decimal places.

a) Based on this model, when barometric pressure is 970 millibars, the wind speed of Atlantic hurricanes is roughly  knots, on average.

b) Based on this model, we are 95% confident that the mean wind speed of all Atlantic hurricanes with a barometric pressure of 970 millibars is between knots and  knots.

c) Based on this model, we are 95% confident that the wind speed of an individual Atlantic hurricane with a barometric pressure of 970 millibars is between knots and  knots

the following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of 20 hurricanes that originated over the Atlantic Ocean in the last decade. A table of summary statistics for this data (as calculated in Homework 9) is also provided below.

In Homework 9, we determined the equation of the least-squares regression line:
y with hat on top equals 1250.350 minus 1.204 x

and also calculated the estimated standard error of the model:
s subscript e equals 7.8660

Use the information given above to complete the following statements. Perform each calculation using a single step in your calculator, and report your answers rounded to 3 decimal places.

a) Based on this model, when barometric pressure is 970 millibars, the wind speed of Atlantic hurricanes is roughly
82.47
knots, on average.

b) Based on this model, we are 95% confident that the mean wind speed of all Atlantic hurricanes with a barometric pressure of 970 millibars is between
knots and
knots.

c) Based on this model, we are 95% confident that the wind speed of an individual Atlantic hurricane with a barometric pressure of 970 millibars is between
knots and
knots

Answer 1

Solution:-

Given that

The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of 20 hurricanes that originated over the Atlantic Ocean in the last decade. A table of summary statistics for this data (as calculated in Homework 9) is also provided below.

a) Based on this model, when barometric pressure is 970 millibars, the wind speed of Atlantic hurricanes is roughly 82.47 knots, on average.

Predicted Y at X = 970 is

b) Based on this model, we are 95% confident that the mean wind speed of all Atlantic hurricanes with a barometric pressure of 970 millibars is between knots and knots.

X value = 970

Confidence level = 95%

Sample size, n = 20

Degrees of freedom, df = n - 2 = 18

Critical value = = 2.101

[excel function:=t.inv.2]

Standard Error of the Estimate, Se = 7.9610

Standard error,

margin of error,

E = 2.1009 * 2.2004

= 4.6229

Confidence Lower limit =

= 82.541 - 4.623

= 77.918

Confidence Upper limit =

= 82.541 + 4.623

= 87.164

c) Based on this model, we are 95% confident that the wind speed of an individual Atlantic hurricane with a barometric pressure of 970 millibars is between knots and knots

For Individual Response Y

Standard error,

margin of error,

E = 2.1009 * 8.26

E = 17.3525

Prediction Interval Lower limit =

= 82.541 - 17.35

= 65.188

Prediction Interval Upper limit =  

= 82.541 - 17.35

= 99.893

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