MATHEMATICS COLLEGE

Law School According to the Law School Admission Council, in the fall of 2007, 66% of law school applicants wereaccepted to some law schooL4 The training program LSATisfaction claims that 163 of the 240 students trained in 2006were admitted to law school. You can safely consider these trainees to be representative of the population of law schoolapplicants. Has LSAﬁsfaction demonstrated a real improvement over the national average?a) What are the hypotheses?b) Check the conditions and ﬁnd the P-value.c) Would you recommend this program based on what you see here? Explain.

Answers

Answer 1

Answer:

Answer:

a) $H_(0): p = 0.66\nH_A: p > 0.66$

b) P-value = 0.2650

c) No, this programme will not be recommended as there is no real improvement over the national average.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 240

p = 66% = 0.66

Alpha, α = 0.05

Number of students admitted to law school , x = 163

a) First, we design the null and the alternate hypothesis

$H_(0): p = 0.66\nH_A: p > 0.66$

This is a one-tailed(right) test.

Formula:

$\hat{p} = (x)/(n) = (163)/(240) = 0.6792$

$z = \frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}$

Putting the values, we get,

$z = \displaystyle\frac{0.6792-0.66}{\sqrt{(0.66(1-0.66))/(240)}} = 0.6279$

b) Now, we calculate the p-value from the table.

P-value = 0.2650

c) Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is no real improvement over the national average.

No, this programme will not be recommended as there is no real improvement over the national average.

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Answers

Answer:

$180

Step-by-step explanation:

Suppose the value of x varies from x = a to x = b . There are at least two ways of thinking about what percent x changed by. We'll explore two of them here. For each of the following questions, write an expression in terms of a and b to answer the question. Method 1 b is how many times as large as a ? times as large Therefore, b is what percent of a ? % Hence, if x varies from x = a to x = b , x changes by what percent?

Answers

The change in the value of x, as a percentage, is given by:

$(b - a)/(a) * 100\%$

The percentage change is given by the change multiplied by 100% and divided by the initial value.

In this question, x varies from $x = a$ to $x = b$ , which means that the initial value is a, and the change is b - a. Then, the percentage chance in the value of x is given by:

$(b - a)/(a) * 100\%$

A similar problem is given at brainly.com/question/24729807

Answer:

Step-by-step explanation:

i. b is how many times as large as a?

b/a

ii. Therefore, b is what percent of a?

b/a*100

iii. Hence, if x varies from x=a to x = b, x changes by what percent?

(100b)/a-100

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) π/2 0 3 1 + cos(x) dx, n = 4

Answers

Split up the integration interval into 4 subintervals:

$\left[0,\frac\pi8\right],\left[\frac\pi8,\frac\pi4\right],\left[\frac\pi4,\frac{3\pi}8\right],\left[\frac{3\pi}8,\frac\pi2\right]$

The left and right endpoints of the $i$ -th subinterval, respectively, are

$\ell_i=\frac{i-1}4\left(\frac\pi2-0\right)=\frac{(i-1)\pi}8$

$r_i=\frac i4\left(\frac\pi2-0\right)=\frac{i\pi}8$

for $1\le i\le4$ , and the respective midpoints are

$m_i=\frac{\ell_i+r_i}2=\frac{(2i-1)\pi}8$

Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

$T_i=\frac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4T_i\approx\boxed{3.038078}$

Midpoint rule

We approximate the area for each subinterval by

$M_i=f(m_i)(\ell_i-r_i)$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4M_i\approx\boxed{2.981137}$

Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

$p_i(x)=f(\ell_i)((x-m_i)(x-r_i))/((\ell_i-m_i)(\ell_i-r_i))+f(m)((x-\ell_i)(x-r_i))/((m_i-\ell_i)(m_i-r_i))+f(r_i)((x-\ell_i)(x-m_i))/((r_i-\ell_i)(r_i-m_i))$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4\int_(\ell_i)^(r_i)p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

$S_i=\displaystyle\int_(\ell_i)^(r_i)p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))$

Then the integral is approximately

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

Final answer:

The question is asking to approximate the definite integral of 1 + cos(x) from 0 to π/2 using the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule for n=4. These are numerical methods used for approximating integrals by estimating the area under the curve as simpler shapes.

Explanation:

This question asks to use several mathematical rules, specifically the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule, to approximate the given integral with a specified value of n which is 4. The integral given is the function 1 + cos(x) dx from 0 to π/2. Each of these rules are techniques for approximating the definite integral of a function. They work by estimating the region under the graph of the function and above the x-axis as a series of simpler shapes, such as trapezoids or parabolas, and then calculating the area of these shapes. The 'dx' component represents a small change in x, the variable of integration. The cosine function in this integral is a trigonometric function that oscillates between -1 and 1, mapping the unit circle to the x-axis. The exact solution would require calculus, but these numerical methods provide a close approximation.

Learn more about Numerical Integration Rules here:

brainly.com/question/36635050

#SPJ11

Help me, please lololol

Answers

9/7 > 1

> is more than
7/7 would be 1

Ralph and Melissa watch lots of videos. But they have noticed that they don't agree very often. In fact, Ralph only likes about 10% of the movies that Melissa likes, i.e., P(Ralph likes a movie|Melissa likes the movie) = .10 They both like about 37% of the movies that they watch. (That is, Ralph likes 37% of the movies he watches, and Melissa likes 37% of the movies she watches.) If they randomly select a movie from a video store, what is the probability that they both will like it? prob. =