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

Multiple Choice

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 $y _ { B } ^ { \prime }$ .