A Marketing Study Was Conducted to Compare the Mean Age $\mathrm { n } = 10 , \quad$

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here:

Female: $\mathrm { n } = 10 , \quad$ sample mean $= 50.30 , \quad$ sample standard deviation $= 13.215$
Male: $\mathrm { n } = 10 , \quad$ sample mean $= 39.80 , \quad$ sample standard deviation $= 10.040$

Find the rejection region to state the correct conclusion when testing at alpha $= 0.01$ .

A) Reject $\mathrm { H } _ { 0 }$ if $\mathrm { t } > 2.528$
B) Reject $\mathrm { H } _ { 0 }$ if $\mathrm { t } > 1.330$
C) Reject $\mathrm { H } _ { 0 }$ if $t > 2.878$
D) Reject $\mathrm { H } _ { 0 }$ if $\mathrm { t } > 2.552$