Solve the following system of equations.
2 answers:
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Answer:
a) Alternative hypothesis should be one sided. Because Null and Alternative hypotheses are:
: μ=2.66 dyne-cm.
: μ<2.66 dyne-cm.
b) the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
Step-by-step explanation:
Let μ be the mean adhesion in dyne-cm.
a)
Null and alternative hypotheses are:
: μ=2.66 dyne-cm.
: μ<2.66 dyne-cm.
b)
First we need to calculate test statistic and then the p-value of it.
test statistic of sample mean can be calculated as follows:
t= where
- X is the sample mean
- M is the mean adhesion assumed under null hypothesis (2.66 dyne-cm)
- s is the standard deviation known (0.7 dyne-cm_2)
- N is the sample size(5)
Sample mean is the average of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm, that is ≈ 3.37
using the numbers we get
t= ≈ 2.27
The p-value is ≈ 0.043. Taking significance level as 0.05, we can conlude that sample proportion is significantly higher than 2.66 dyne-cm.
Thus, according to the sample the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
<h3>Answer: See the attached image below</h3>
It shows your screenshot, but I've filled in the blanks with the answers.
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Explanation:
Positive integers represent yards that the team gains. On the opposite side, negative integers represent yards the team loses.
For example, if a team gains 3 yards, then we write that as +3 or simply 3. If a team loses 5 yards, then we write -5. Adding 3 to -5 gets us 3+(-5) = -2 showing the overall result is a loss of 2 yards at the end of the second down.
As another example, if a team gains 7 yards on first down, but then loses those 7 yards on second down, then they gained overall 7+(-7) = 0 yards overall. They haven't gone anywhere at the end of the second down.
We could do things the other way around like this. Suppose the team loses 8 yards on first down, but has better luck on second down to gain 8 yards. They get back to the original line of scrimmage (back to the starting point) and we can say -8+8 = 0. The team hasn't gone anywhere, but it could be worse and they could be dealing with a loss of yardage.
It might help to set up a vertical number line to help try to visualize negative numbers. Each gain means you go upward. Each loss means you go downward. In a sense, it's like a skyscraper and each integer represents floors of the building. Negative integers are basement floors. Zero is the ground level.