24 The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains.t 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 a local newspaper thought that it would be of interest to her readers to conduct a similar study for restaurants located in her city. 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. Italian Seafood Steakhouse $12 $16 $25 14 18 19 14 16 24 16 25 24 18 24 22 21 16 22 17 18 27 11 37 Use a = 0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. State the null and alternative hypotheses. O H: Not all the population means are equal. H PItalian HSeafood Steakhouse O Ho: HItalian * HSeafood Psteakhouse H Pitalian 'Seafood -Steakhouse O Ho: HItalian =Seafood Steakhouse H: Not all the population means are equal. O Ho: HItalian=Seafood HSteakhouse H: Pitalian Seafood steakhouse O H: At least two of the population means are equal. H: At least two of the population

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The second slide is the first part of the question  and the first slide is the second part of the question.

### Statistical Testing Exercise

**Find the value of the test statistic.**

\[ \_\_\_ \]

**Find the \( p \)-value. (Round your answer to four decimal places.)**

\[ p\text{-value} = \_\_\_\_ \]

**What is your conclusion?**

- \( \circ \) Reject \( H_0 \). There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.
- \( \circ \) Do not reject \( H_0 \). There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.
- \( \circ \) Do not reject \( H_0 \). There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.
- \( \circ \) Reject \( H_0 \). There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.
Transcribed Image Text:### Statistical Testing Exercise **Find the value of the test statistic.** \[ \_\_\_ \] **Find the \( p \)-value. (Round your answer to four decimal places.)** \[ p\text{-value} = \_\_\_\_ \] **What is your conclusion?** - \( \circ \) Reject \( H_0 \). There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants. - \( \circ \) Do not reject \( H_0 \). There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants. - \( \circ \) Do not reject \( H_0 \). There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants. - \( \circ \) Reject \( H_0 \). There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.
**Restaurant Price Analysis**

**Introduction:**
The Consumer Reports Restaurant Customer Satisfaction Survey provides insights based on 148,599 visits to full-service restaurant chains. A notable metric from this survey is the meal price—the average amount paid per person. With an interest in offering relevant information to readers, a local newspaper reporter decided to conduct a similar study focusing on restaurants in her city. The following data presents the meal prices ($) from 24 different restaurant samples, categorized into three types: Italian, Seafood, and Steakhouse.

**Data:**

|          | Italian | Seafood | Steakhouse |
|----------|---------|---------|------------|
| **Meals**| 24      | 17      | 21         |
|          | 11      | 18      | 16         |
|          | 24      | 18      | 22         |
|          | 37      | 27      | 22         |
|          |         |         |            |
| **Costs**| $12     | $16     | $25        |
|          | $16     | $14     | $19        |

**Analysis Objective:**
The study aims to determine if there is a statistically significant difference among the mean meal prices across these three restaurant categories. A significance level of \(\alpha = 0.05\) is used for hypothesis testing.

**Hypotheses:**
- Null Hypothesis (\(H_0\)): All population means are equal.
- Alternative Hypothesis (\(H_a\)): Not all the population means are equal.

\(o\) \(H_0\): \(\mu_{Italian} = \mu_{Seafood} = \mu_{Steakhouse}\)
\(o\) \(H_a\): At least two of the population means are different. 

**Conclusion:**
Upon conducting the test, results will determine if diners can expect a difference in meal pricing based on the type of restaurant chosen. This analysis provides valuable insights for consumers making dining decisions and for restaurateurs positioning their pricing strategies.
Transcribed Image Text:**Restaurant Price Analysis** **Introduction:** The Consumer Reports Restaurant Customer Satisfaction Survey provides insights based on 148,599 visits to full-service restaurant chains. A notable metric from this survey is the meal price—the average amount paid per person. With an interest in offering relevant information to readers, a local newspaper reporter decided to conduct a similar study focusing on restaurants in her city. The following data presents the meal prices ($) from 24 different restaurant samples, categorized into three types: Italian, Seafood, and Steakhouse. **Data:** | | Italian | Seafood | Steakhouse | |----------|---------|---------|------------| | **Meals**| 24 | 17 | 21 | | | 11 | 18 | 16 | | | 24 | 18 | 22 | | | 37 | 27 | 22 | | | | | | | **Costs**| $12 | $16 | $25 | | | $16 | $14 | $19 | **Analysis Objective:** The study aims to determine if there is a statistically significant difference among the mean meal prices across these three restaurant categories. A significance level of \(\alpha = 0.05\) is used for hypothesis testing. **Hypotheses:** - Null Hypothesis (\(H_0\)): All population means are equal. - Alternative Hypothesis (\(H_a\)): Not all the population means are equal. \(o\) \(H_0\): \(\mu_{Italian} = \mu_{Seafood} = \mu_{Steakhouse}\) \(o\) \(H_a\): At least two of the population means are different. **Conclusion:** Upon conducting the test, results will determine if diners can expect a difference in meal pricing based on the type of restaurant chosen. This analysis provides valuable insights for consumers making dining decisions and for restaurateurs positioning their pricing strategies.
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