Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was
1 answer:
Answer:
There is no convincing evidence at α = 0.10 level that the average vertical jump of students at this school differs from 15 inches.
Step-by-step explanation:
We have to make a hypothesis test to prove the claim that the average vertical jump of students differs from 15 inches.
The null and alternative hypothesis are:
The significance level is 0.10.
The sample mean is 17 and the sample standard deviation is 5.37.
The degrees of freedom are df=(20-1)=19.
The t-statistic is:
The two-sided P-value for t=1.67 is P=0.11132.
This P-value is bigger than the significance level, so the effect is not significant. The null hypothesis can not be rejected.
There is no convincing evidence at α = 0.10 level that the average vertical jump of students at this school differs from 15 inches.
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Answer:
a) 20 ways
b) 10 ways
Step-by-step explanation:
When the order of selection/choice matters, we use Permutations to find the number of ways and if the order of selection/choice does not matter, we use Combinations to find the number of ways.
Part a)
We have to chose 2 objects from a group of 5 objects and order of choice matters. This is a problem of permutations, so we have to find 5P2
General formula of permutations of n objects taken r at time is:
Using the value of n=5 and r=2, we get:
Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice matters.
Part b)
Order of choice does not matter in this case, so we will use combinations to find the number of ways of choosing 2 objects from a group of 5 objects which is represented by 5C2.
The general formula of combinations of n objects taken r at a time is:
Using the value of n=5 and r=2, we get:
Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice does not matters.
The volume formula of a cone is 
the r is the radius and h is the height. However, if you multiply by pi, you will get an approximated volume of the cone. So we will multiply like this for now. 
Don't worry, we'll use pi in the end.
I'm going to assume that 7 inches is your radius. We need to plug in 7 for r and 4 in for h into the equation. Once we do that, it will look like this.
means we will need to divide one by 3. That gives us 0.33333... now we have to multiply by 
we get 16.33333... now the last thing we need to do is multiply by 4, which is h. We get 65.33333. Add pi and you have your answer. 
I'm going to assume that 7 inches is your radius. We need to plug in 7 for r and 4 in for h into the equation. Once we do that, it will look like this.