Nacirema Airlines is buying a fleet of new fuel$-$efficient planes. The HogJet and the LitheJet both meet their price and performance needs, and both planes meet EPA noise guidelines. However, the quieter plane is preferred. Each plane is flown through a typical takeoff and landing sequence $10$ times, while remote sensors at ground level record the noise levels $($in decibels$).$ The table below summarizes the sound level tests using Excel$$s default level of significance $(\backslash$alpha $=\mathrm{.}05).$

t$-$Test Assuming Equal Variances

LitheJet HogJet

Mean $80\mathrm{.}336882\mathrm{.}4669$

Variance $0\mathrm{.}71784\mathrm{.}7385$

Observations $1010$

Pooled Variance $2\mathrm{.}7282$

Hypothesized Diff $0\mathrm{.}0000$

df $18$

t Stat $2\mathrm{.}8837$

P$($T $<=$ t$)$ one$-$tail $0\mathrm{.}0049$

t Critical one$-$tail $1\mathrm{.}7341$

P$($T $<=$ t$)$ two$-$tail $0\mathrm{.}0099$

t Critical two$-$tail $2\mathrm{.}1009$

t$-$Test Assuming Unequal Variances

LitheJet HogJet

Mean $80\mathrm{.}336882\mathrm{.}4669$

Variance $0\mathrm{.}71784\mathrm{.}7385$

Observations $1010$

Hypothesized Diff $12$

df $0$

t Stat $2\mathrm{.}8837$

P$($T $<=$ t$)$ one$-$tail $0\mathrm{.}0069$

t Critical one$-$tail $1\mathrm{.}7823$

P$($T $<=$ t$)$ two$-$tail $0\mathrm{.}0137$

t Critical two$-$tail $2\mathrm{.}1778$

In a left$-$tailed test comparing the means at $\backslash$alpha $=\mathrm{.}05,$ we would

Multiple Choice

not reject H$0.$

reject H$0.$

have insufficient information to make a decision.

reject H$1.$