5.43 Chicken diet and weight, Part III: In Exercises 5.31 and 5.33 we compared the effects of two types of feed at a time. A better analysis would first consider all feed types at once: casein, horsebean, linseed, meat meal, soybean, and sunflower. The ANOVA output below can be used to test for differences between the average weights of chicks on different diets. DF Sum Sq Mean Sq F value Pr(>F) feed 5 231129.16 46225.83 15.36 0.0000 residuals 65 195556.02 3008.55 Conduct a hypothesis test to determine if these data provide convincing evidence that the average weight of chicks varies across some (or all) groups. Make sure to check relevant conditions. Figures and summary statistics are shown below. What are the hypotheses for this test? ( )Ho: μc = μh = μl = μm = μsoy = μsun Ha: At least one pair of means is the same ( )Ho: μc = μh = μl = μm = μsoy = μsun Ha: At least one of the means is different ( )Ho: μc = μh = μl = μm = μsoy = μsun Ha: μc ≠ μh ≠ μl ≠ μm ≠ μsoy ≠ μsun The test statistic for the hypothesis test is:___________ (please round to two decimal places) The p-value for the hypothesis test is: ____________ (please round to four decimal places) Interpret the result of the hypothesis test in the context of the study: ( )Since p < α, we reject the null hypothesis and accept that the average weight of chicks is different for each type of diet ( )Since p < α, we reject the null hypothesis and accept that the average weight of chicks is the same across all of the diets ( )Since p < α, we reject the null hypothesis and accept that the average weight of chicks is not the same across all of the diets ( )Since p = 0, there is no chance that the average weight of chicks is the same across all of the diets
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
5.43 Chicken diet and weight, Part III: In Exercises 5.31 and 5.33 we compared the effects of two types of feed at a time. A better analysis would first consider all feed types at once: casein, horsebean, linseed, meat meal, soybean, and sunflower. The ANOVA output below can be used to test for differences between the average weights of chicks on different diets.
| DF | Sum Sq | Mean Sq | F value | Pr(>F) | |
|---|---|---|---|---|---|
| feed | 5 | 231129.16 | 46225.83 | 15.36 | 0.0000 |
| residuals | 65 | 195556.02 | 3008.55 |
Conduct a hypothesis test to determine if these data provide convincing evidence that the average weight of chicks varies across some (or all) groups. Make sure to check relevant conditions. Figures and summary statistics are shown below.
What are the hypotheses for this test?
- ( )Ho: μc = μh = μl = μm = μsoy = μsun
Ha: At least one pair of means is the same - ( )Ho: μc = μh = μl = μm = μsoy = μsun
Ha: At least one of the means is different - ( )Ho: μc = μh = μl = μm = μsoy = μsun
Ha: μc ≠ μh ≠ μl ≠ μm ≠ μsoy ≠ μsun
The test statistic for the hypothesis test is:___________ (please round to two decimal places)
The p-value for the hypothesis test is: ____________ (please round to four decimal places)
Interpret the result of the hypothesis test in the context of the study:
- ( )Since p < α, we reject the null hypothesis and accept that the average weight of chicks is different for each type of diet
- ( )Since p < α, we reject the null hypothesis and accept that the average weight of chicks is the same across all of the diets
- ( )Since p < α, we reject the null hypothesis and accept that the average weight of chicks is not the same across all of the diets
- ( )Since p = 0, there is no chance that the average weight of chicks is the same across all of the diets
Consider that μc, μh, μl, μm, μsoy and μsun are the average weights of chicks of feed types of casein, horsebean, linseed, meat meal, soybean, and sunflower, respectively.
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