Question two Taken directly from the unit notes. 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 5.2 3.4 8 10 1.5 Hours of exercise/week 8.6 8.1 8.5 7.4 6.8 9.4 7.7 a. Sketch a scatter plot for the data, is the relationship linear? b. What is the correlation between the two variables? c. Calculate the coefficient of determination and explain. 6. 2. 9,
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Do only question 3
![Question two
* Taken directly from the unit notes.
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
5.2
2
3.4
8
10
1.5
needed/night
Hours of
exercise/week
8.6
9
8.1
8.5
7.4
6.8
9.4
7.7
a. Sketch a scatter plot for the data, is the relationship linear?
b. What is the correlation between the two variables?
c. Calculate the coefficient of determination and explain.
Question three
* Taken directly from the unit notes.
a. Using the same data from question two, calculate and interpret the regression line
for the dit.
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