Answer: The p-value is 0.154.
Step-by-step explanation:
Since we have given that
We claim that
Null hypothesis :

Alternate hypothesis :

Population mean = 20 hours
Sample mean = 18.5 hours
Sample standard deviation = 4.3 hours
Sample size n = 35
So, test statistic would be

So, the p value would be 0.154.
Hence, the p-value is 0.154.
For the given situation we have a total of 259,459,200 permutations.
<h3>
How many permutations are?</h3>
First, how we know that it is a permutation?
Because the order matters, we aren't only selecting 8 out of the 15 people, but these 8 selected also have an order (is not the same thing to finish the race first than fourth, for example).
Then we need to find the number of permutations, to do it, we need to find the numbers of options for each of the 8 positions.
- For the first position there are 15 options.
- For the second position ther are 14 options (one runner already finished).
- For the third position there are 13 options.
- And so on.
Then the total number of permutations (product between the numbers of options) is:
P = 15*14*13*12*11*10*9*8 = 259,459,200
If you want to learn more about permutations:
brainly.com/question/11732255
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Find the possible rational roots and use synthetic division to find the first zero.
I chose x=1 (which represents the factor "x-1")
1║2 -7 -13 63 -45
║ 2 -5 -18 45
2 -5 -18 45 0
(x-1) is a factor, (2x³ - 5x² - 18x + 45) is the other factor.
Use synthetic division on the decomposed polynomial to find the next zero.
I chose x = 3 (which represents the factor "x-3")
3║2 -5 -18 45
║ 6 3 -45
2 1 -15 0
Using synthetic division, we discovered that (x-1), (x-3), & (2x² + x -15) are factors. Take the new decomposed polynomial (2x² + x -15) and find the last two factors using any method.
Final Answer: (x-1)(x-3)(x+3)(2x-5)
You should pat a total of $90.44