The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Construct a 95% prediction interval for y, the number of days absent, given x = 95
Degrees,? = 0.449x - 30.27 and $\mathrm { s } _ { \mathrm { e } }$ = 0.934. Round interval to three decimal places. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, } \mathrm { y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$$
A) $9.957

Question

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Construct a 95% prediction interval for y, the number of days absent, given x = 95
Degrees,? = 0.449x - 30.27 and $\mathrm { s } _ { \mathrm { e } }$ = 0.934. Round interval to three decimal places. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, } \mathrm { y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$$
A) $9.957 < y < 14.813$
B) $3.176 < y < 5.341$
C) $4.321 < y < 6.913$
D) $6.345 < y < 8.912$

Quizplus · Accepted Answer

To construct a 95% prediction interval for y given x = 95, we first calculate the predicted value of y using the given regression equation: ŷ = 0.449(95) - 30.27 = 12.885. The prediction interval formula is ŷ ± t*se, where t is the t-value for 95% confidence with n-2 degrees of freedom (n is the number of pairs, so n-2 = 10-2 = 8), and se is the standard error of the estimate. Without the exact t-value provided, we can't calculate the exact interval here, but the correct interval must be centered around the predicted value of 12.885, which option A is the only one that reasonably fits this criteria, assuming a typical t-value for 95% confidence with 8 degrees of freedom.

The Data Below Are the Temperatures on Randomly Chosen Days se\mathrm { s } _ { \mathrm { e } }se​

The Data Below Are the Temperatures on Randomly Chosen Days $\mathrm { s } _ { \mathrm { e } }$