Question two A researcher is proposing that exercise makes a person more energized as a result they require less sleep. He carries out a survey on the number of hours of exercise per week and the average hours of sleep needed per night in order to feel well rested. The results are shown on page 2 for the 8 participants. Average hours of sleep needed/night 4 5.2 2 3.4 8 10 1.5 6 Hours of exercise/week 8.6 8.1 9 8.5 7.4 6.8 9.4 7.7 Sketch a scatter plot for the data, is the relationship linear? What is the correlation between the two variables? Calculate the coefficient of determination and explain.
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.
Question two
A researcher is proposing that exercise makes a person more energized as a result they require less sleep. He carries out a survey on the number of hours of exercise per week and the average hours of sleep needed per night in order to feel well rested. The results are shown on page 2 for the 8 participants.
|
Average hours of sleep needed/night |
4 |
5.2 |
2 |
3.4 |
8 |
10 |
1.5 |
6 |
|
Hours of exercise/week |
8.6 |
8.1 |
9 |
8.5 |
7.4 |
6.8 |
9.4 |
7.7 |
- Sketch a
scatter plot for the data, is the relationship linear? - What is the
correlation between the two variables? - Calculate the coefficient of determination and explain.
. Explain the following steps involved in a chi-square test of independence:
- i) Identify the claim then state the null and alternative hypotheses (Ho and Ha) for this test.
ii)Select the level of significance.
iii) Calculate the test statistic.
iv) Formulate the Decision Rule and Make a Decision.
v) Interpret your decision in terms of the claim.
Question three
- Using the same data from question two, calculate and interpret the regression line for the data.
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