A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced 63 62 43 43 58 59 67 61 Sprout Percent 55.1 62.4 64.1 74.1 63.6 66.3 51.9 64.7 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are: `H0: ` ? μ r ρ == 0 `Ha:` ? r μ ρ ≠≠ 0 The p-value is: (Round to four decimal places) Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
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.
A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below.
| Seeds Produced | 63 | 62 | 43 | 43 | 58 | 59 | 67 | 61 |
|---|---|---|---|---|---|---|---|---|
| Sprout Percent | 55.1 | 62.4 | 64.1 | 74.1 | 63.6 | 66.3 | 51.9 | 64.7 |
- Find the
correlation coefficient : r=r= Round to 2 decimal places. - The null and alternative hypotheses for correlation are:
`H0: ` ? μ r ρ == 0
`Ha:` ? r μ ρ ≠≠ 0
The p-value is: (Round to four decimal places) - Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
- There is statistically significant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds.
- There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use of the regression line is not appropriate.
- There is statistically insignificant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds.
- There is statistically significant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the regression line is useful.
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