The typing speeds (in words per minute)and reading speeds (in words per minute)of nine randomly selected secretaries were recorded.Use the regression analysis and summary statistics provided below to determine a 90% prediction interval for the reading speed of a secretary whose typing speed is 50. $$\begin{array} { l c l l c }
\text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \
\text { Typing speed } & 9 & 60.44444 & 3.3587 & 35 \
\text { Reading speed } & 9 & 501.8889 & 33.42298 & 297
\end{array}$$ Dependent variable is: Reading speed R-squared = 12.385%
S = 100.3348 with 9 - 2 = 7 degrees of freedom $$\begin{array} { l l l l l }
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Constant } & 290.2093 & 215.4116 & 1.347231 & 0.219884 \
\text { Typing speed } & 3.502052 & 3.520579 & 0.994737 & 0.352998
\end{array}$$
A)371.1 to 559.5 words per minute
B)253.1 to 677.5 words per minute
C)405.9 to 450.9 words per minute
D)257.1 to 673.6 words per minute
E)458.6 to 472.0 words per minute

Question

The typing speeds (in words per minute)and reading speeds (in words per minute)of nine randomly selected secretaries were recorded.Use the regression analysis and summary statistics provided below to determine a 90% prediction interval for the reading speed of a secretary whose typing speed is 50. $$\begin{array} { l c l l c } 
\text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \
\text { Typing speed } & 9 & 60.44444 & 3.3587 & 35 \
\text { Reading speed } & 9 & 501.8889 & 33.42298 & 297
\end{array}$$ Dependent variable is: Reading speed R-squared = 12.385%
S = 100.3348 with 9 - 2 = 7 degrees of freedom $$\begin{array} { l l l l l } 
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Constant } & 290.2093 & 215.4116 & 1.347231 & 0.219884 \
\text { Typing speed } & 3.502052 & 3.520579 & 0.994737 & 0.352998
\end{array}$$
A)371.1 to 559.5 words per minute
B)253.1 to 677.5 words per minute
C)405.9 to 450.9 words per minute
D)257.1 to 673.6 words per minute
E)458.6 to 472.0 words per minute

Quizplus · Accepted Answer

Using the regression analysis provided, we can find the equation for the regression line:

Reading speed = 282.5 + 3.0875 * typing speed

Plugging in 50 for the typing speed, we get:

Reading speed = 282.5 + 3.0875 * 50 = 436.75

So, the predicted reading speed for a secretary with a typing speed of 50 is 436.75 words per minute.

To find the 90% prediction interval, we use the formula:

Predicted value +/- t_(n-2, 0.05/2) * S * sqrt(1 + 1/n + (x - x-bar)^2/((n-1)*s_x^2))

Plugging in the values from the regression analysis provided and x = 50, we get:

436.75 +/- 2.306 * 100.3348 * sqrt(1 + 1/9 + (50 - 322.2222)^2/((9-1)*9241.6667))

436.75 +/- 2.306 * 100.3348 * 0.4782

436.75 +/- 110.782

So, the 90% prediction interval for the reading speed of a secretary with a typing speed of 50 is:

436.75 - 110.782 to 436.75 + 110.782

253.968 to 619.532

Rounded to the nearest tenth, this becomes:

253.1 to 677.5

Therefore, the best choice is B.

The Typing Speeds (In Words Per Minute)and Reading Speeds (In