Question

Dave loves Japanese food. Among the Japanese restaurants in Champaign, he especially likes Sakanaya and Miga. Dave believes that there is no difference in the amount of money Dave spends at Sakanaya and Miga. But his friends thinks he spends more money at one place than the other. Being a statistician, Dave wants to collect data and conduct a hypothesis test to make a decision. He randomly goes to one of the 2 restaurants and records the bill each time.

In his data, Dave went to Sakanaya 35 times and his bills there have a mean of 19.5 dollars and a standard deviation of 5.3 dollars. On the other hand, Dave went to Miga 34 times and his bills there have a mean of 22.75 dollars and a standard deviation of 9.55 dollars.

Assume that the amount on each bill is independent from one another. Also assume that the population standard deviations of the amount of money Dave spends at Sakanaya and Miga are the same.

Do a hypothesis test and state your conclusion. Use the significance level  = 0.025.

Which of the following is the correct ?

(a) The difference in the population averages = 0

(b) Both population averages = 0

(c) The difference in the sample averages = 0

(d) Both sample average = 0

Choose the correct alternative hypothesis .

(a) The difference in the population averages  0

(b) Both population averages  0

(c) The difference in the sample averages  0

(d) Both sample averages  0

Compute the test statistic for the test that you chose above.

Test statistic:

Make sure your answer contains exactly 2 digits after the decimal point.

Use your rounded answer for question 3 and the table to compute the p-value.

p-value:

Make sure your answer contains at least 4 digits after the decimal point.

Which of the following is the correct conclusion?

(a) We fail to reject Dave's claim and concludes there is no evidence supporting for a difference in the average amount of money Dave spends on eating out at Sakanaya and Miga.

(b) We fail to reject Dave's claim and concludes that there is a difference in the average amount of money Dave spends on eating out at Sakanaya and Miga.

(c) We reject Dave's claim and concludes that there is a difference in the average amount of money Dave spends on eating out at Sakanaya and Miga.

(d) We reject Dave's claim and concludes there is no evidence supporting for a difference in the average amount of money Dave spends on eating out at Sakanaya and Miga.

Answer 1