Question

Geoff is the proud owner of a restaurant. He is interested in determining whether his Wagyu beef or Hiramasa kingfish sashimi should be marketed as the Geoff Special. Geoff has selected a random sample of 20 people to taste his Wagyu beef and give it a score out of 100. He also selected a different random sample of 20 people to taste his Hiramasa kingfish sashimi and give it a score out of 100.

The sample mean score given to the Wagyu beef dish was calculated as 68.96. The sample standard deviation of the scores for the Wagyu beef dish was calculated as 4. The sample mean score given to the Hiramasa kingfish sashimi dish was calculated as 63.09. The sample standard deviation of the scores for the Hiramasa kingfish sashimi dish was calculated as 4. The population standard deviations of the scores for each dish are unknown.

You may find this Student's t distribution table useful 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 with H₀: μ_W = μ_H and H_A: μ_W ≠ μ_H. Calculate the test statistic (t) for this hypothesis test. Give your answer to 2 decimal places.

t = 4.64 is this correct

b)Using the test statistic for Geoff's hypothesis test and a 95% confidence level, Geoff should not reject, reject, or accept

the null hypothesis.

Answer 1

a) Test statistic

where

= 4

Therefore

= 5.87/1.2649

= 4.64

b) degrees of freedom =20+20-2=38

Using critical value approach

Using 95% confidence , that is

two tailed critical value of t with 38 df is

tc = 2.024 ( critical value obtained from t table )

Since calculated t > tc

We reject H0.

There is sufficient evidence to conclude that mean scores of each of the dishes are not equal .