Harry took out a loan from the bank. the variable ddd models harry's remaining debt (in dollars) ttt months after he took out th
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Answer:
Option b.
Step-by-step explanation:
Given : is right angled triangle . An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of S R is x.
In the figure, and RT is perpendicular to SQ.
We know that in a right angled triangle if a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the perpendicular are similar to each other and to the whole triangle .
Therefore ,
Also, we know that if two triangles are similar then their sides are proportional .
So, option b. is correct
Answer:
Step-by-step explanation:
Hello!
Your study variable is
X: Number of students that finished tha statistics course with an a, in a sample of 100 students.
This variable has a binomial distribution X~Bi(n;ρ)
The student believes that no more than 20% of the students pass the course with an A. This percentage is the population proportion symbolically: ρ ≤ 0.20, and is your null hypothesis., so:
a.
H₀: ρ ≤ 0.20
H₁: ρ > 0.20
α: 0,01
The statistic to use is the Z approximation for the proportions. To assemble this statistic, the central limit theorem is applied, this theorem allows us, at a sufficiently large sample size (n≥30), to approximate the distribution of the sample proportion (^p) to normal:
^p ≈ N(p; p(1-p)(1/n))
The statistic formula is:
Z=<u> ^p - p </u>≈ N(0;1)
√p(1-p)(1/n)
the sample proportion is ^p= 0.24
b.
Z=<u> 0.24 - 0.2 </u>= 1
√0.2*0.8(1/100)
The rejection region of this hypothesis is one-tailed (positive) If you ever have trouble identifying the type of rejection region look at the direction of the alternative hypothesis, if it has the symbol < then is a one-tailed, to the left, rejection region. If it has the symbol > then is a one-tailed, to the right, rejection region and if it has the ≠ symbol, it means the rejection region is "split" in two, i.e. two-tailed.
The critical value is:
If Z ≥ 2.33, then you reject the null hypothesis.
If Z < 2.33, then you do not reject the null hypothesis.
The decision is to not reject the null hypothesis.
c.
The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
Symbolically:
P(Z ≥ 1) = 1 - P(Z < 1) = 1 - 0.84134 = 0.15866
You have to look at what is the probability of the calculated Z value, the direction of the p-value is always the same as the rejection region. In this case, is a one-tailed p-value (to the right)
Using the p-value approach, the decision rule is always the same:
If p-value ≤ α, then you reject the null hypothesis.
If p-value > α, then you don't reject the null hypothesis.
Since the p-value 0.15866 > 0.01, then you do not reject the null hypothesis.
As expected, using the two methods you reached the same decision. If not then you have to check your maths.
I hope it helped!