Italian 12 13 15 17 18 20 17 24 Seafood 16 18 17 26 23 15 19

Italian: 12, 13, 15, 17, 18, 20, 17, 24

Seafood: 16, 18, 17, 26, 23, 15, 19, 18

Steakhouse: 24, 19, 23, 25, 21, 22, 27, 31

Suppose a reporter wanted to study the average meal price for restaurants located in Myrtle Beach, South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. This dataset shows the prices obtained for the 24 restaurants sampled. Use = 0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurant. *Give your answers to two decimal places.*

1. What is the null hypothesis ?

2. What is MSTR?

3. What is MSE? *Give your answer to two decimal places.*

4. What is the value of the test statistic? *Give your answer to two decimal places.*

5. What is the p-value? *Give your answer to four decimal places.*

6. What is your conclusion using = 0.05?

7. State your conclusion in words a non-statistician could understand.

Solution

One-way ANOVA: Italian, Seafood, Steakhouse

Source DF SS MS F P
Factor 2 208.0 104.0 7.33 0.004
Error 21 298.0 14.2
Total 23 506.0

S = 3.767 R-Sq = 41.11% R-Sq(adj) = 35.50%

Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev ---------+---------+---------+---------+
Italian 8 17.000 3.854 (-------*------)
Seafood 8 19.000 3.703 (-------*-------)
Steakhouse 8 24.000 3.742 (-------*------)
---------+---------+---------+---------+
17.5 21.0 24.5 28.0

Pooled StDev = 3.767

1) Null hyothesis: All three restaurent means are equal

2)MSTR is defined as the l treatment sum of squares/ degress of freedom = treatement sum of squares/ (3-1) =104

3. MSE = Mean square error = SSE/N-K = 298/21 = 142

4. test statistic = 7.33

5. P-value =0. 004

6. P-value is less than 0.05 so reject null hypothesis

7. The average meal prices of three types of restuarents are not equal