10.59 To tip or not to tip. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether the customer left a tip.12 There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip. a. Find the proportion of tippers for the red-shirted servers and the proportion of tippers for the servers with other colored shirts. b. Find a 95% confidence interval for the difference in proportions. à. Give a null hypothesis for this setting in terms of the parameters. Explain the meaning of the null hypothesis in simple terms. b. Give an alternative hypothesis for this setting in terms of the parameters. Explain the meaning of the alternative hypothesis in simple terms. Give a reason for your choice of this particular alternative hypothesis. c. Are the conditions satisfied for the use of the significance test based on the Normal distribution? Explain your answer.
10.59 To tip or not to tip. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether the customer left a tip.12 There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip. a. Find the proportion of tippers for the red-shirted servers and the proportion of tippers for the servers with other colored shirts. b. Find a 95% confidence interval for the difference in proportions. à. Give a null hypothesis for this setting in terms of the parameters. Explain the meaning of the null hypothesis in simple terms. b. Give an alternative hypothesis for this setting in terms of the parameters. Explain the meaning of the alternative hypothesis in simple terms. Give a reason for your choice of this particular alternative hypothesis. c. Are the conditions satisfied for the use of the significance test based on the Normal distribution? Explain your answer.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Tipping Behavior Study: Shirt Color and Tipping Rates
**Study Overview**
The study examined the relationship between the color of the shirt worn by a server and the likelihood of receiving a tip from the customer. The study included 418 male customers in total.
- **Red Shirt:** Of the 69 customers served by someone wearing a red shirt, 40 left a tip.
- **Other Colors:** Of the 349 customers served by someone wearing a different colored shirt, 130 left a tip.
**Questions and Analyses**
1. **Proportions and Confidence Interval**
a. **Proportion of Tippers**
- Calculate the proportion of customers who tipped for both scenarios (red-shirted servers vs. other colored shirts).
b. **Confidence Interval**
- Compute a 95% confidence interval for the difference in tipping proportions between the two groups.
2. **Hypotheses**
a. **Null Hypothesis**
- Define the null hypothesis in terms of tipping proportions and explain its meaning simply.
b. **Alternative Hypothesis**
- Define the alternative hypothesis similarly and provide reasoning for its selection.
3. **Conditions for Normal Distribution**
- Assess whether the conditions for applying a significance test based on the Normal distribution are satisfied.
4. **Statistical Testing**
a. **Distribution of Test Statistic**
- Describe the expected distribution of the test statistic under the null hypothesis.
b. **Find the Test Statistic**
- Calculate the test statistic for the given scenario.
c. **P-value**
- Determine the P-value associated with the test statistic.
d. **Interpretation with Normal Distribution**
- Utilize a sketch of a Normal distribution to explain the interpretation of the found P-value.
This exercise involves statistical analysis to determine if there is a significant difference in tipping behavior based on the server's shirt color.
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