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% confidence interval for the average reading speed of a secretary whose typing speed is 71. $$\begin{array} { l c l l c }
\text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \
\text { Typing speed } & 9 & 60.44444 & 3.3587 & 35 \
\text { Reading speed } & 9 & 501.8889 & 33.42298 & 297
\end{array}$$ 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)330.4 to 747.3 words per minute
B)444.1 to 633.6 words per minute
C)532.2 to 545.5 words per minute
D)405.9 to 450.9 words per minute
E)326.4 to 751.3 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% confidence interval for the average reading speed of a secretary whose typing speed is 71. $$\begin{array} { l c l l c } 
\text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \
\text { Typing speed } & 9 & 60.44444 & 3.3587 & 35 \
\text { Reading speed } & 9 & 501.8889 & 33.42298 & 297
\end{array}$$ 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)330.4 to 747.3 words per minute
B)444.1 to 633.6 words per minute
C)532.2 to 545.5 words per minute
D)405.9 to 450.9 words per minute
E)326.4 to 751.3 words per minute

Quizplus · Accepted Answer

We want to find the 90% confidence interval for the average reading speed of a secretary whose typing speed is 71. We can use the regression equation:

Reading speed = intercept + slope * typing speed

From the summary statistics provided, we know that the slope is 1.9568 and the intercept is 184.6682. Thus, the equation is:

Reading speed = 184.6682 + 1.9568 * typing speed

Substituting typing speed = 71, we get:

Reading speed = 184.6682 + 1.9568 * 71 = 320.9818

Now, we need to find the standard error of the estimate. From the summary statistics provided, we know that S = 100.3348. The standard error of the estimate is:

SE = S / sqrt(n) = 100.3348 / sqrt(9) = 33.4449

To find the 90% confidence interval, we use the t-distribution with 7 degrees of freedom (n-2). From the t-table or calculator, the t-value for a 90% confidence interval and 7 degrees of freedom is 1.895. The 90% confidence interval is:

320.9818 ± 1.895 * 33.4449 = [ 279.0860 , 362.8776 ]

Therefore, the best choice is B, which gives the interval 444.1 to 633.6 words per minute.

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