Answer:
[0.841;6.879]
Step-by-step explanation:
Hello!
You have two independent samples:
Sample 1
X₁: tree species in an unlogged plot.
n₁= 12 plots
Unlogged 22 18 22 20 15 21 13 13 19 13 19 15
Sample 2
X₂: tree species in a plot logged 8 years earlier
n₂= 9
Logged 17 4 18 14 18 15 15 10 12
The objective of this experiment is to estimate the difference between the means of the number of species on the unlogged plots and the logged plots. Symbolically: μ₁-μ₂
To be able to estimate the difference between the two population means, I'll assume that both variables have a normal distribution and use a pooled t-statistic for the Confidence interval. (I did a quick F-test for variance homogeneity, population variances are unknown but equal)
The formula is:
(X₁[bar]-X₂[bar])±*(Sₐ√(1/n₁+1/n₂))
Where
sample mean sample 1 X₁[bar]= 17.50
sample mean sample 2 X₂[bar]= 13.64
S₁= 3.53
S₂= 4.50
Sₐ²= <u>(n₁ - 1)S₁² + (n₂ - 1)S₂² </u>= <u>11*(3.53)² + 8*(4.50)² </u>= 15.74
n₁+n₂-2 19
Sₐ= 3.96
Now replace the values in the formula:
(X₁[bar]-X₂[bar])±*(Sₐ√1/n₁+1/n₂)
[(17.50-13.64) ± 1.729*(3.96*√(1/12+1/9))]
[3.86 ± 3.019]
[0.841;6.879]
With a confidence level of 90%, you'd expect that the interval [0.841;6.879] contains the difference between the means of the number of species on the unlogged plots and the logged plots.
I hope it helps!
a, b, c - side lengths (a ≤ b ≤ c)
If , then is Obtuse triangle.
If , then is Right triangle.
If , then Acute triangle.
Check to see if the sum of the first two sides is greater than the third.
, therefore is Scalene triangle.
It's Obtuse triangle.
Answer:
Distance = 21 miles.
Step-by-step explanation:
Let x be the distance in miles between the airport and Ann's home.
We have been given that Ann took a taxi home from the airport. The taxi fare was $2.10 per mile. So fare for x miles will be 2.10x.
We are also told that she gave the driver a tip of $5. Ann paid a total of $49.10. This means that fare of x miles and tip given to driver equals $49.10. We can represent this information in an equation as:
Now let us solve our equation.
Therefore, the equation represents the distance in miles between the airport and Ann's home and distance between Ann's home and airport in 21 miles.
Answer:
Step-by-step explanation:
Check attachment for diagram
From the diagram, we can apply Pythagoras theorem to right angle triangle RPS
Then,
Tan θ = opposite / adjacent
Tan θ = 15 / 15
Tan θ = 1
θ = arcTan(1)
θ = 45°
The angle is between the east and south
Then, the bearing of 45°S of east.
The direction is also β
Where
β + θ = 360°
β + 45 = 360°
β = 360 - 45
β = 315°
Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solutio to the problem
Let X the random variable that represent the amount of beer in each can of a population, and for this case we know the distribution for X is given by:
Where and
For this case we select 6 cans and we are interested in the probability that the total would be less or equal than 72 ounces. So we need to find a distribution for the total.
The definition of sample mean is given by:
If we solve for the total T we got:
For this case then the expected value and variance are given by:
And the deviation is just:
So then the distribution for the total would be also normal and given by:
And we want this probability:
And we can use the z score formula given by: