What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below. Time 0 5 4 4 14 16 7 5 2 Score 42 55 59 59 84 83 59 73 66 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are: H0:H0: ? μ ρ r == 0 H1:H1: ? ρ μ r ≠≠ 0 The p-value is: (Round to four decimal places)
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.
What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below.
| Time | 0 | 5 | 4 | 4 | 14 | 16 | 7 | 5 | 2 |
|---|---|---|---|---|---|---|---|---|---|
| Score | 42 | 55 | 59 | 59 | 84 | 83 | 59 | 73 | 66 |
- Find the
correlation coefficient : r=r= Round to 2 decimal places. - The null and alternative hypotheses for correlation are:
H0:H0: ? μ ρ r == 0
H1:H1: ? ρ μ r ≠≠ 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 student who spends more time studying will score higher on the final exam than a student who spends less time studying.
- There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful.
- There is statistically insignificant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the use of the regression line is not appropriate.
- There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying.
- r2r2 = (Round to two decimal places)
- Interpret r2r2 :
- Given any group that spends a fixed amount of time studying per week, 71% of all of those students will receive the predicted score on the final exam.
- There is a 71% chance that the regression line will be a good predictor for the final exam score based on the time spent studying.
- 71% of all students will receive the average score on the final exam.
- There is a large variation in the final exam scores that students receive, but if you only look at students who spend a fixed amount of time studying per week, this variation on average is reduced by 71%.
- The equation of the linear regression line is:
ˆyy^ = + xx (Please show your answers to two decimal places) - Use the model to predict the final exam score for a student who spends 10 hours per week studying.
Final exam score = (Please round your answer to the nearest whole number.) - Interpret the slope of the regression line in the context of the question:
- The slope has no practical meaning since you cannot predict what any individual student will score on the final.
- As x goes up, y goes up.
- For every additional hour per week students spend studying, they tend to score on averge 2.16 higher on the final exam.
- Interpret the y-intercept in the context of the question:
- The y-intercept has no practical meaning for this study.
- The best prediction for a student who doesn't study at all is that the student will score 51 on the final exam.
- The average final exam score is predicted to be 51.
- If a student does not study at all, then that student will score 51 on the final exam.
Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately.
1.
Correlation between Time score is,
r=0.84, from the excel function, =CORREL(A2:A10,B2:B10)
2.
Null Hypothesis:
Alternative Hypothesis:
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