Report an appropriate hypothesis test for a positive linear relationship and use a 5% significance level.Explain the power of the test in words, in context.In the answer options below I have used the phrase “a certain relationship” because I don’t want to give away exactly what type of relationship it is.Group of answer choicesThe power of the test is the probability of accepting that there is a certain relationship between Sale amount and Tip when actually there isn’t.The power of the test is the probability of not accepting that there is a certain relationship between Sale amount and Tip when actually there is.The power of the test is the probability of accepting that there is a certain relationship between Sale amount and Tip when indeed there is.The power of the test is the probability of not accepting that there is a certain relationship between Sale amount and Tip when indeed there isn’t. **Analysis of Sales and Tips at Sonny’s Restaurant***Overview:*The graph and the Excel summary output below display weekend sales and tips at Sonny’s restaurant in Tallahassee, FL. This data is used to address specific questions in the context of the study.*Data Source:*The data was collected by Sonny’s employee, Joshua Gonzalez, for a group project in the STA 2122 class during the Summer of 2007.**SLRI Sonny’s Scatterplot:***Scatterplot Description:*- The scatterplot displays a relationship between the sale amount in dollars (x-axis) and the tips in dollars (y-axis) at Sonny's restaurant.- A trend line is drawn to show the general direction of the data.- Various data points are marked (A through H), representing individual observations of sales and tips.*Key Observations:*- The trend line suggests a positive correlation: as sales increase, tips tend to increase.- There are outlier points such as point A, which has lower sales and tips, and point H, which shows higher sales and tips.**Summary Output:***Regression Statistics:*- **Multiple R**: 0.58064672 (Measure of the correlation between observed and predicted values)- **R Square**: 0.337150613 (Proportion of variance in the dependent variable explained by the independent variable)- **Adjusted R Square**: 0.325722175 (Adjusted version of R Square considering the number of predictors)- **Standard Error**: 28.73607083 (Average distance that the observed values fall from the regression line)- **Observations**: 60 (Total number of data points)These statistical outputs provide insights into the strength and reliability of the relationship between sales and tips at Sonny’s restaurant, indicating a moderate positive correlation. **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**Explanation:**- **ANOVA Table**: Displays analysis of variance of the regression model. - **df**: Degrees of freedom for regression and residual. - **SS**: Sum of Squares due to regression and residual. - **MS**: Mean Square due to regression (calculated as SS/df for regression). - **F**: F-statistic for testing significance of the regression model. - **Significance F**: P-value for the F-statistic.- **Coefficients Table**: Presents the coefficients of the regression variables. - **Coefficients**: Estimates for Intercept and Sale Amount. - **Standard Error**: Standard deviation of the coefficient estimates. - **t Stat**: t-statistic for testing the null hypothesis that the coefficient is zero. - **P-value**: Probability that the observed t-statistic (or more extreme) is observed under the null hypothesis. - **Lower 95%** and **Upper 95%**: 95% confidence

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.Explain the power of the test in words, in context.In the answer options below I have used the phrase “a certain relationship” because I don’t wa