# Statistically analyze differences between urban and suburban restaurants for variables.

See attached data file.

Assignment 6

Measuring Differences Between Two Means (1)

Go to the Resources section in this syllabus and open the file restaurants.xls. This data file contains ratings for food, decor, service, and the price per person for a sample of 50 restaurants located in an urban area and 50 restaurants located in a suburban area.

Statistically analyze the differences between urban and suburban restaurants for the variables food rating, decor rating, service rating, and price per person. All tests should be conducted at the 95% confidence level. Make sure to state the null and alternative hypotheses, your statistical decision based on the outcomes (reject or fail to reject the null), and your pragmatic interpretation of the results.

Please copy and paste your statistical output and answers in a word processing file.

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#### Solution Preview

See the attached files.

General Discussion

In this problem we are asked to analyze statistically, whether there exists significant difference between urban and suburban restaurants with respect to a number of variables. The procedure for the analysis is as follows:

Null Hypothesis There is no significant difference between urban and suburban restaurants with respect to certain variable under consideration.

Alternative Hypothesis There is significant difference between urban and suburban restaurants with respect to certain variable under consideration.

Symbolically the null and alternative hypotheses can be expressed as follows.

against

where - mean value of the variable under consideration of urban restaurants and - mean value of the variable under consideration of suburban restaurants.

The test statistic is where

- sample mean of the urban values ; - sample mean of the suburban values; - sample variance of the urban values ; - sample variance of the suburban values ; sample size of the urban data and sample size of the suburban data

The test statistic follows student's t distribution with degrees of freedom

The rejection region is , where is the critical value taken from student's t tables with degrees of freedom at (1- ) 100% confidence level. This means if the absolute value of't' is greater than the critical value we reject the null hypothesis, otherwise we ...

#### Solution Summary

This solution is set-up and includes calculations and interpretation of the results in an attached Word and Excel file.