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 below 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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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 below 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.
Step by step
Solved in 2 steps with 4 images
