Two researchers run identical experiments except researcher A collects twice as many points as researcher B. For a specific value $x$, researcher A estimates a $y$ value of $y _ { A } ^ { \prime }$ and researcher B estimates a $y$ value of $y _ { B ^ { \prime } }$. We would expect that researcher $\mathrm { A } ^ { \prime } \mathrm { s } 95 \%$ prediction interval around $y _ { A } ^ { \prime }$ to be, in general,

A) wider than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$ or narrower than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$, with equal probability.
B) the same as researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$.
C) narrower than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime } { } _ { B }$.
D) wider than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$.

Question

Two researchers run identical experiments except researcher A collects twice as many points as researcher B. For a specific value

x

, researcher A estimates a

y

value of

y _ { A } ^ { \prime }

and researcher B estimates a

y

value of

y _ { B ^ { \prime } }

. We would expect that researcher

\mathrm { A } ^ { \prime } \mathrm { s } 95 \%

prediction interval around

y _ { A } ^ { \prime }

to be, in general,

A) wider than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$ or narrower than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$, with equal probability.
B) the same as researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$.
C) narrower than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime } { } _ { B }$.
D) wider than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$.

Quizplus · Accepted Answer

Collecting more data points generally leads to more precise estimates, resulting in narrower prediction intervals. Therefore, researcher A's 95% prediction interval around $y_A'$ would be expected to be narrower than researcher B's, due to the larger sample size.

Two Researchers Run Identical Experiments Except Researcher a Collects Twice xxx

Two Researchers Run Identical Experiments Except Researcher a Collects Twice $x$