Geoff is the proud owner of a restaurant. He is interested in determining whether hisWagyu beeforHiramasa kingfish sashimishould be marketed as theGeoff Special. Geoff has selected a random sample of 20 people to taste hisWagyu beefand give it a score out of 100. He also selected a different random sample of 20 people to taste hisHiramasa kingfish sashimiand give it a score out of 100.

The sample mean score given to theWagyu beefdish was calculated as 67.14. The sample standard deviation of the scores for theWagyu beefdish was calculated as 5. The sample mean score given to theHiramasa kingfish sashimidish was calculated as 66.8. The sample standard deviation of the scores for theHiramasa kingfish sashimidish was calculated as 4. The population standard deviations of the scores for each dish are unknown.

You may find thisStudent's t distribution tableuseful throughout the following questions. Note that Geoff always aims to use the easiest possible calculations, and so when using a two-sample t-test he will use the simplified formula for degrees of freedom whenever possible.

a)Geoff would like to test whether the mean scores of each of these dishes are equal. He has constructed a hypothesis test withH₀: _W= _HandH_A: _{W H}. Calculate the test statistic (t) for this hypothesis test. Give your answer to 2 decimal places.

t =

b)Using the test statistic for Geoff's hypothesis test and a 90% confidence level, Geoff should

accept, reject, or not rejectthe null hypothesis.