Geoff is the proud owner of a restaurant. He is interested in determining whether his Wagyu...

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 65.64. The sample standard deviation of the scores for the Wagyu beef dish was calculated as 3. The sample mean score given to the Hiramasa kingfish sashimi dish was calculated as 60.56. The sample standard deviation of the scores for the Hiramasa kingfish sashimi dish was calculated as 3. 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 =

b)Using the test statistic for Geoff's hypothesis test and a 90% confidence level, Geoff should accept, reject, not reject the null hypothesis.

Solutions

Expert Solution

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Wagyu beef dish	20	65.64	3.00	0.67
Hiramasa kingfish sashimi dish	20	60.56	3.00	0.67

test statistic t =

S_p = pooled standard deviation =

Estimation for Difference

Difference	Pooled StDev
5.080	3.000

test statistic t = 5.35

df = n1+n2-2 = 20+20 - 2= 38

b) at 90% confidence level alpha = 0.1

critical value = t_0.05,38 = 1.686

Since we test statistic is greater than critical value we reject null hypothesis and conclude that there is a significant difference between the mean scores of the dishes.

orchestra answered 1 year ago

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