Questions: The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consume Reports website). One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for the Sun Coast Times thought that it would be of interest to her readers to conduct a similar study for restaurants located on the Grand Strand section in Myrtle Beach, South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices () obtained for the 24 restaurants sampled. Use α=0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. Italian Seafood Steakhouse 10 15 22 12 17 18 15 15 23 16 25 25 18 25 19 22 15 24 15 21 28 26 17 32

The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consume Reports website). One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for the Sun Coast Times thought that it would be of interest to her readers to conduct a similar study for restaurants located on the Grand Strand section in Myrtle Beach, South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices () obtained for the 24 restaurants sampled. Use α=0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. Italian Seafood Steakhouse 10 15 22 12 17 18 15 15 23 16 25 25 18 25 19 22 15 24 15 21 28 26 17 32
Transcript text: The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consume Reports website). One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for the Sun Coast Times thought that it would be of interest to her readers to conduct a similar study for restaurants located on the Grand Strand section in Myrtle Beach, South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices $(\$)$ obtained for the 24 restaurants sampled. Use $\alpha=0.05$ to test whether there is a significant difference among the mean meal price for the three types of restaurants. \begin{tabular}{ccc} Italian & Seafood & Steakhouse \\ $\$ 10$ & $\$ 15$ & $\$ 22$ \\ $\$ 12$ & $\$ 17$ & $\$ 18$ \\ $\$ 15$ & $\$ 15$ & $\$ 23$ \\ $\$ 16$ & $\$ 25$ & $\$ 25$ \\ $\$ 18$ & $\$ 25$ & $\$ 19$ \\ $\$ 22$ & $\$ 15$ & $\$ 24$ \\ $\$ 15$ & $\$ 21$ & $\$ 28$ \\ $\$ 26$ & $\$ 17$ & $\$ 32$ \end{tabular}
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the Sum of Squares

To perform the one-way ANOVA, we first calculate the sum of squares between groups and within groups.

The sum of squares between groups is given by: \[ SS_{between} = \sum_{i=1}^k n_i (\bar{X}_i - \bar{X})^2 = 216.0833 \]

The sum of squares within groups is calculated as: \[ SS_{within} = \sum_{i=1}^k \sum_{j=1}^{n_i} (X_{ij} - \bar{X}_i)^2 = 467.875 \]

Step 2: Calculate Mean Squares

Next, we compute the mean squares for both between and within groups.

The mean square between groups is: \[ MS_{between} = \frac{SS_{between}}{df_{between}} = \frac{216.0833}{2} = 108.0417 \]

The mean square within groups is: \[ MS_{within} = \frac{SS_{within}}{df_{within}} = \frac{467.875}{21} = 22.2798 \]

Step 3: Calculate the F-Statistic

The F-statistic is calculated using the mean squares: \[ F = \frac{MS_{between}}{MS_{within}} = \frac{108.0417}{22.2798} = 4.8493 \]

Step 4: Calculate the P-Value

The p-value is determined from the F-distribution: \[ P = 1 - F(F_{observed}; df_{between}, df_{within}) = 1 - F(4.8493; 2, 21) = 0.0186 \]

Step 5: Conclusion

With a significance level of \(\alpha = 0.05\), we compare the p-value to \(\alpha\):

  • Since \(P = 0.0186 < 0.05\), we reject the null hypothesis.

This indicates that there is a significant difference among the mean meal prices for the three types of restaurants.

Final Answer

\(\boxed{\text{Reject the null hypothesis: There is a significant difference among the mean meal prices for the three types of restaurants.}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which of the lines in the following graph appear to be tangent lines? Select all that apply. A. L5 B. L6 C. L4 E. L1 Why do the lines, selected above, appear to be tangent lines, and why are the other line(s) not tangent lines? - A. The slope of each selected tangent line appears to be undefined. The other line(s) are parallel to the graph at the point of tangency. - B. Each tangent line is perpendicular to the graph at the point of intersection between the graph and the respective tangent line. The other line(s) are not perpendicular to the graph at the point. - C. The slope of each tangent line is equal to the slope of the graph at the point of intersection between the graph and the respective tangent line. The other line(s) are not parallel to the graph at the point of tangency. - D. The slope of each tangent line is approximately zero. The slope(s) of the other line(s) are undefined.
failedAnswered
Subtract. -4-(-8)= 7-(-7)=
failedAnswered
© 2022 Chamberlain University Heart Valves Which valve prevents the backflow of blood into the right ventricle? Aortic valve Mitral valve Pulmonary valve Tricuspid valve Bicuspid valve
failedAnswered
The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions (a) through (e) 60 25 41 47 44 9 (a) Compute the population mean, μ μ= (Type an integer or a decimal)
failedAnswered
You wish to test the following claim (Ha) at a significance level of α=0.001. For the context of this problem, d= new - old where the first data set represents the rating for an old product and the second data set represents the scores for the new product. Ho: μd=0 Ha: μd<0 You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: old new --- --- 50.6 0.3 49 40.6 59.5 25.2 59.1 39.5 57 33.3 47.7 23 What is the test statistic for this sample? (Report answer accurate to three decimal places.) t= The p -value is ... This p -value leads to a decision to... - reject the null - accept the null - fail to reject the null