Question

Meteorologists are interested in the relationship between minimum pressure and maximum wind speed of hurricanes. The minimum pressure, in millibars, and maximum wind speed, in knots, were collected for a random sample of 100 hurricanes from the year 1995 to the year 2012. A regression analysis of maximum wind speed on minimum pressure produced a 95 percent confidence interval of (1.42,-1.20) for the slope of the between least-squares regression line. Which statement is a correct interpretation of the interval?

(A) The probability is 0.95 that wind speed will decrease, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure .
(B) The probability is 0.95 that a different sample of 100 hurricanes will result in an increase, on average, of wind speed between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.
(C) We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.
(D) We can be 95% confident that wind speed increases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure .
(E) We can be 95% confident that, for any sample of hurricanes, the wind speed will decrease, on average 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

Answer 1

(C) We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

Explanation:

Given the interval :

(-1.42,-1.20)

The interval here depicts a decrease I the rate or change. That is the slope value is negative and hence there is a reduction in the response varibale per unit increase in the independent variable.

The range of WINDSPEED Given is 1.20 knots to 1.42 knots

Hence, the interpretation goes thus ; at 95% confidence interval ;

We can be 95% confident that response varibale decreases on average, between 1.20 to 1.42 for every unit increase in the independent variable.