Report an appropriate hypothesis test for a positive linear relationship and use a 5% significance level.The P-value is [ Select ] ["low", "not very low"] so we [ Select ] ["conclude", "cannot conclude"] that there is [ Select ] ["a linear", "no linear", "a positive linear", "a negative linear"] relationship between [ Select ] ["predicted sale amount and predicted tip", "average sale amount and tip", "average sale amount and average tip", "predicted sale amount and tip", "sale amount and tip"] . **Educational Website Content: Analysis of Weekend Sales and Tips at Sonny's Restaurant****Introduction:**The information below presents data on weekend sales and tips at a Sonny's restaurant in Tallahassee, FL. This analysis is based on data gathered by Joshua Gonzalez, an employee at Sonny's, for a group project in the Summer 2007 STA 2122 class.**Scatterplot Explanation:**The scatterplot titled "SLRI SONNY'S SCATTERPLOT" shows the relationship between sales amount (x-axis) and tips (y-axis). Data points are marked, with a fitted line illustrating the trend. Specific points are labeled A to H, indicating outliers or points of interest in the data. The general trend suggests a positive correlation between sale amounts and tips received.**Summary Output:**The following regression statistics provide insight into the data:- **Multiple R:** 0.58064672 - Indicates a moderate correlation between sales and tips. - **R Square:** 0.337150613 - Suggests that approximately 33.7% of the variability in tips can be explained by the sales amount. - **Adjusted R Square:** 0.325722175 - An adjustment of the R Square, considering the number of predictors in the model. - **Standard Error:** 28.73607083 - Represents the average distance that the observed values fall from the regression line. - **Observations:** 60 - Indicates the number of data points used in the analysis.This analysis helps in understanding the factors influencing tips and informs strategies for enhancing customer service and sales strategies. ### ANOVA Table| | df | SS | MS | F | Significance F ||----|----|-------------|-------------|--------------|-----------------|| Regression | 1 | 24360.81754 | 24360.81754 | 29.50102381 | 1.15405E-06 || Residual | 58 | 47894.18246 | 825.7617666 | | || Total | 59 | 72255 | | | |### Coefficients Table| | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% ||---------------|--------------|----------------|-------------|-------------|---------------|---------------|| Intercept | 56.95659334 | 12.27319518 | 4.640730674 | 2.02919E-05 | 32.38912416 | 81.52406252 || Sale Amount | 0.126993685 | 0.023381027 | 5.431484494 | 1.15405E-06 | 0.080191475 | 0.173795894 |© 2020 Radha Bose Florida State University Department of Statistics### ExplanationThe above tables represent the results of an ANOVA (Analysis of Variance) and regression analysis on a dataset. **ANOVA Table:**- **df (Degrees of Freedom):** The number of values in the final calculation of a statistic that are free to vary. - **SS (Sum of Squares):** A measure of the total variability in the data.- **MS (Mean Square):** The average of the squares of the differences between the observed and estimated values.- **F:** The ratio of the model mean square to the error mean square.- **Significance F:** The p-value for the F-test, determining if there is a statistically significant difference.**Coefficients Table:**- **Coefficients:** Represent the change in the dependent variable for a one-unit change in the predictor variable.- **Standard Error:** The standard deviation of the sampling distribution of the coefficients.- **t Stat:** The statistic for testing the null hypothesis that the coefficient is equal to zero.- **

Name: Report an appropriate hypothesis test for a positive linear relationsh
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Report an appropriate hypothesis test for a positive linear relationship and use a 5% significance level.The P-value is [ Select ] ["low", "not very low"] so we

The hypothesis to test for the positive linear relationship between sales amount and tip is given below : Ho : There is no relationship between the two. ρ=0H1 : There is a positive relationship between the two. ρ>0 The p-value is 1.15405E-06 = 0.00000115405 The decision rule states, if p-value is less than alpha level of significance then reject the null hypothesis, accept otherwise. 0.00000115405<0.05 - Reject Null hypothesis Concluding that there is a positive linear relationship between the two variables.The p-value is "low" so we "conclude" that there is "a positive linear" relationship between "sales amount and tip".