Use the t-distribution to find a confidence interval for a mean μ given the relevant sample results. Give the best point estimate for μ, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed.1. A 90% confidence interval for μ using the sample results x^- =143.0, s=56.7, and n=50Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.i. point estimate = ii. margin of error = iii. The 90% confidence interval is_______ to _________.

Answer:

$854.90

Step-by-step explanation:

List Price Before Tax = $778.95

Sales Tax Rate = 9.75% = 0.0975

Total Cost of the Camera = ?

Sales Tax = List Price Before Tax x Sales Tax Rate

Sales Tax = $778.95 x 9.75%

Sales Tax = $75.9476

or

Sales Tax = $75.95

Now add the Sales Tax in List Price Before Tax, to compute the Total Cost of the Camera, as follows;

Total Cost of the Camera = Sales Tax + List Price Before Tax

Total Cost of the Camera = $75.95 + $778.95

Total Cost of the Camera = $854.90

Step-by-step explanation:

A,B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:1 of A IS AT (-1,9) and B (2,0)

to find out point C use section formula

[tex](\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]

A is (-1,9) that is our (x1,y1)

that is our (x2,y2)

ratio is 1:1 that is m and n

Plug in the values in the formula

[tex](\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]

[tex](\frac{1(x_2)+1(-1)}{1+1} ,\frac{1(y_2)+1(9)}{1+1} ) =(2,0)\\\frac{1(x_2)+1(-1)}{1+1}=2\\\frac{1(x_2)+1(-1)}{2}=2\\\\x_2-1=4\\x_2= 5\\\frac{1(y_2)+1(9)}{1+1}=0 \\\frac{1(y_2)+1(9)}{2} =0\\\\y_2+9=0\\x_2= -9[/tex]

Answer C is (5,-9)

Answer:

[tex]\frac{50}{3}[/tex] cm/sec.

Step-by-step explanation:

We have been given that a particle in the first quadrant is moving along a path described by the equation [tex]x^2+xy+2y^2=16[/tex] such that at the moment its x-coordinate is 2, its y-coordinate is decreasing at a rate of 10 cm/sec. We are asked to find the rate at which x-coordinate is changing at that time.

First of all, we will find the y value, when [tex]x =2[/tex] by substituting [tex]x =2[/tex] in our given equation.

[tex]2^2+2y+2y^2=16[/tex]

[tex]4-16+2y+2y^2=16-16[/tex]

[tex]2y^2+2y-12=0[/tex]

[tex]y^2+y-6=0[/tex]

[tex]y^2+3y-2y-6=0[/tex]  

[tex](y+3)(y-2)=0[/tex]

[tex](y+3)=0,(y-2)=0[/tex]

[tex]y=-3,y=2[/tex]

Since the particle is moving in the 1st quadrant, so the value of y will be positive that is [tex]y=2[/tex].

Now, we will find the derivative of our given equation.

[tex]2x\cdot x'+x'y+xy'+4y\cdot y'=0[/tex]

We have been given that [tex]y=2[/tex], [tex]x =2[/tex] and [tex]y'=-10[/tex].

[tex]2(2)\cdot x'+(2)x'+2(-10)+4(2)\cdot (-10)=0[/tex]

[tex]4\cdot x'+2x'-20-80=0[/tex]

[tex]6x'-100=0[/tex]

[tex]6x'-100+100=0+100[/tex]

[tex]6x'=100[/tex]

[tex]\frac{6x'}{6}=\frac{100}{6}[/tex]

[tex]x'=\frac{50}{3}[/tex]

Therefore, the x-coordinate is increasing at a rate of [tex]\frac{50}{3}[/tex] cm/sec.

9514 1404 393

Answer:

  w = 250m

Step-by-step explanation:

As the problem statement tells you, the independent variable, the number of minutes he reads, causes a change in the dependent variable, the number of words read. This is modeled by ...

  w = 250m

Answer: B. w = 250m

Step-by-step explanation: i answered the question and got it right :)

Answer:

16

Step-by-step explanation:

Answer:

16, AKA C

Step-by-step explanation:

Edge 2021 :)

Answer:

{(5,3) , (6,1), (7,-1), (8,-3)}

Step-by-step explanation:

inverse of (x,y) is (y,x)

inverse of { (3,5), (1, 6), ( -1, 7), (-3, 8)} is

{(5,3) , (6,1), (7,-1), (8,-3)}

Answer:

8x-32

Step-by-step explanation:

Because 8 multiples X and gives 8x and also multiples-4 and gives you -32

:.8x-32

Answer:

The value of z test statistics for the appropriate hypothesis test is 1.90.

Step-by-step explanation:

We are given that the response times of technicians of a large heating company follow a Normal distribution with a standard deviation of 10 minutes.

He takes a random sample of 25 response times and calculates the sample mean response time to be 33.8 minutes.

Let [tex]\mu[/tex] = mean response time.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30 minutes     {means that the mean response time is 30 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 minutes     {means that the mean response time has increased from the target of 30 minutes}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

                        T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean response time = 33.8 minutes

            [tex]\sigma[/tex] = population standard deviation = 10 minutes

            n = sample of response times = 25

So, test statistics  =  [tex]\frac{33.8-30}{\frac{10}{\sqrt{25} } }[/tex]  

                               =  1.90

Hence, the value of z test statistics for the appropriate hypothesis test is 1.90.

Answer:

Base= 5.09 cm x 5.09 cm; height = 1.69 cm

Step-by-step explanation:

-> materials has a square base of side length, dimension will be: x . x = x²

'y' represents height

->For dimensions of 4 silver plated sides= xy each

->dimensions of the nickel plated top= x²

Volume = yx²

44=yx² => y= 44/x²

Cost of the sides will be( 4 * xy * $3 )

Cost of the top and the bottom will be  (2 * x² * $1)

For the Total cost: 12xy + 2x²

substituting value of 'y' in above equation,

=> Total cost = 12x (44/x²) + 2x² = 528 / x + 2x²

To Minimum critical point => d [cost] / dx = 0

=> - 528/x² + 4x =0

132/x² - x =0

132 - x³ = 0

x³ = 132

Taking cube root on both sides

∛x³ = ∛(132)

x= 5.09

=> y = 44/5.09² =>1.69

Dimensions of the box :

Base= 5.09 cm x 5.09 cm; height = 1.69 cm

Answer:

1/50 times 2/99 = 2/4950

divide numerator and denominator by 2 and the answer you should get is 1/2475 and in decimal form it equals 0.00040404040404040

Step-by-step explanation:

Step-by-step explanation:

A question is asked with options for answers, but in reality, there is only one question stating that it is correct.

Answer:

Length of arc=4π

Step-by-step explanation:

Length of arc=¤/360 x 2xπxr

Where:

¤=72

r=10

Length of arc=72/360 x 2xπx10

Length of arc=0.2 x 20π

Length of arc=4π

Answer:

2

Step-by-step explanation:

f=1

2 x 1=2

4-2=2

Answer:2

Step-by-step explanation:

If f=1 then that means you are multiplying 2 by 1 which is 2. So that makes your problem 4-2=2

4-2(1)=2

Answer:

2/6 or 1/3

Step-by-step explanation:

3 and 6 are multiples of 3

so that is 2 out of 6 numbers on a fair dice.

Answer: V = 343unit³

Step-by-step explanation:

This is a solid shape problems a three dimensional.

Surface area of a cube = 6s² and the Volume = s³.

Since the surface area is given to be 294, we now use this to calculate the s.

Now,

6s² = 294, now solve for s

s² = 294/6

= 49

s² = 49

Now, to find s, we recalled the laws of indices by taking the square root of both sides

√s² = +/- √49

s. = +/-7unit.

Now to find the volume of the cube, where

V = s³ and s = 7, therefore

V = 7³

= 343unit³

Answer:

 P = 0.688

Step-by-step explanation:

Since x= 1764, n = 2565

95%. CI= ( 0.670, 0.706)

a) P=  x/n

   P = 1764/2565

   P = 0.688

Answer:

25.3%

Step-by-step explanation:

Let P be the percent

Of means multiply and is means equals

P *75 = 19

Divide each side by 75

P* 75/75 = 19/75

P =.25333333

Change from decimal to percent form

P = 25.33333333%

Rounding to one decimal

25.3%

Answer:

25.3

Step-by-step explanation:

19/75 = 0.253

0.253 x 100% = 25.3%

Answer:

y=-6x+7    (Negative Slope)

Step-by-step explanation:

This equation is in slope intercept form.

7= y-intercept

-6= slope

This means that when you plot this on a graph, your slope will be negative.

Answer:

a. We fail reject to the null hypothesis because zo = -5.84 < 1.65 = zα and P-value = 1 (approximately)

b. The confidence Interval for u1 - u2 is; 6.79 ≤ u1 - u2

c. The power of the test = 1 -

β = 0.998736

d. The sample size is adequate because the power of the test is approximately 1

Step-by-step explanation:

Given

Standard Deviations; σ1 = σ2 = 1.0 psi

Size: n1 = 10; n2 = 12

X = 162.5; Y = 155.0

Let X1, X2....Xn be a random sample from Population 1

Let Y1, Y2....Yn be a random sample from Population 2

We assume that both population are normal and the two are independent.

Therefore, the test statistic

Z = (X - Y - (u1 - u2))/√(σ1²/n1 + σ2²/n2)

See attachment for explanation

The p-value is 0.028, indicating that plastic 1's breaking strength exceeds that of plastic 2 by at least 10 psi. A 95% confidence interval for the difference in means is (4.858, 22.142). The power of the test is 0.858, indicating a high probability of correctly rejecting the null hypothesis. The sample sizes employed may not be adequate to detect a difference of 12 psi.

To determine whether the electronics component manufacturer should use plastic 1, we will conduct a Hypothesis testing and calculate a confidence interval for the difference in means.

(a) We will test the null hypothesis that the mean breaking strength of plastic 1 is less than or equal to the mean breaking strength of plastic 2 by at least 10 psi.

Using a t-test, we find the p-value to be 0.028.

Since this is less than the significance level of 0.05, we reject the null hypothesis and conclude that plastic 1's breaking strength exceeds that of plastic 2 by at least 10 psi.

(b) To calculate a 95% confidence interval for the difference in means, we use the formula: difference in means ± (t-value * standard error).

With a true difference in means of 12 psi, the confidence interval is (4.858, 22.142).

(c) The power of a test is the probability of correctly rejecting the null hypothesis when it is false.

We can calculate the power using the formula: 1 - Beta. Given alpha = 0.05, the power of the test is 0.858.

(d) To determine if the sample sizes are adequate, we can calculate the minimum sample size required to detect a difference of 12 psi with a power of at least 0.8.

Using a power analysis, we find that a sample size of 16 for each type of plastic would be adequate.

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Answer:

(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.

(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

Step-by-step explanation:

Let X = number of heads.

The probability that a head occurs in a toss of a coin is, p = 0.50.

The coin was tossed n = 100 times.

A random toss's result is independent of the other tosses.

The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.50.

But the sample selected is too large and the probability of success is 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of [tex]\hat p[/tex] (sample proportion of X) if the following conditions are satisfied:

Check the conditions as follows:

 [tex]np=100\times 0.50=50>10\\n(1-p)=100\times (1-0.50)=50>10[/tex]

Thus, a Normal approximation to binomial can be applied.

So,  [tex]\hat p\sim N(p,\ \frac{p(1-p)}{n})[/tex]

[tex]\mu_{p}=p=0.50\\\sigma_{p}=\sqrt{\frac{p(1-p)}{n}}=0.05[/tex]

(a)

Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:

[tex]P(0.30<\hat p<0.70)=P(\frac{0.30-0.50}{0.05}<\frac{\hat p-p}{\sigma_{p}}<\frac{0.70-0.50}{0.05})\\[/tex]

                              [tex]=P(-4<Z<4)\\=P(Z<4)-P(Z<-4)\\=(\approx1)-(\approx0)\\=1[/tex]

Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.

(b)

Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:

[tex]P(0.40<\hat p<0.65)=P(\frac{0.40-0.50}{0.05}<\frac{\hat p-p}{\sigma_{p}}<\frac{0.65-0.50}{0.05})\\[/tex]

                              [tex]=P(-2<Z<3)\\=P(Z<3)-P(Z<-2)\\=0.9987-0.0228\\=0.9759[/tex]

Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.

Through the Law of Large Numbers, we can approximated the binomial distribution with a normal distribution when the number of repetitions is quite high. We find the mean and standard deviation for the distribution and convert the asked proportion of heads to equivalent X and Z values. The probabilities are found by referring to a Standard Normal Distribution Table.

In this problem, we are dealing with a binomial distribution -- a coin flip with two outcomes, heads or tails. But since the number of flips is high (100), we can use Normal approximation to solve the problem.

Whenever a fair coin is tossed, the chance of getting a head is 0.5. This is our theoretical probability, which doesn't guarantee exact outcomes but gives an estimated figure when the size of event repetitions is high. The main principle here is the Law of Large Numbers, which states that as the number of repetitions of an experiment increases, we expect the empirical probability to approach the theoretical probability.

Let's calculate the mean (μ) and standard deviation (σ) for this distribution.

(a) To find the probability of the sample proportion of heads being between 0.3 and 0.7, we convert these into equivalent X values and then find the corresponding Z values.

We calculate Z for each using Z = (X - μ) / σ. After that, we refer to the Z table (Standard Normal Distribution Table) or use a calculator to find the probabilities.

Repeat similar steps for part (b) for the probabilities between 0.4 and 0.65.

Note: While using Normal approximation, we apply a Continuity Correction factor of ±0.5 depending upon the problem.

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Answer:

Maximum value: [tex] 3* \sqrt{n} [/tex]

Minimum value: [tex] -3* \sqrt{n} [/tex]

Step-by-step explanation:

Let [tex] g(x) = x_1^2 + x_2^2+x_3^2+ ----+ x_n^2[/tex] , the restriction function.The Lagrange Multiplier problem states that an extreme (x1, ..., xn) of f with the constraint g(x) = 9 has to follow the following rule:

[tex] \nabla{f}(x_1, ..., x_n) = \lambda \nabla{g} (x_1,...,x_n) [/tex]

for a constant [tex] \lambda [/tex] .

Note that the partial derivate of f respect to any variable is 1, and the partial derivate of g respect xi is 2xi, this means that

[tex] 1 = \lambda 2 x_1 [/tex]

Thus,

[tex] x_i = \frac{1}{2\lambda} = c [/tex]

Where c is a constant that doesnt depend on i. In other words, there exists c such that (x1, x2, ..., xn) = (c,c, ..., c). Now, since g(x1, ..., xn) = 9, we have that n * c² = 9, or

[tex] c = \, ^+_- \, \sqrt{\frac{9}{n} } = \, ^+_- \frac{3}{\sqrt{n}} [/tex]

When c is positive, f reaches a maximum, which is [tex]  \frac{3}{\sqrt{n}}  +  \frac{3}{\sqrt{n}} +  \frac{3}{\sqrt{n}}  + ..... +  \frac{3}{\sqrt{n}}  = n *  \frac{3}{\sqrt{n}}  = 3 * \sqrt{n} [/tex]

On the other hand, when c is negative, f reaches a minimum, [tex]-3 * \sqrt{n} [/tex]

Answer:

(a)0.5

(b)0.625

Step-by-step explanation:

Out of 100 MBA students

Total Sample Space, n(S)=100

(a)Let event A be the event  that an MBA student has at least four years of work experience.

n(A)=15+35=50

Therefore:

[tex]P(A)=\dfrac{n(A)}{n(S)} =\dfrac{50}{100}=0.5[/tex]

The probability that this student has at least four years of work experience is 0.5.

(b)Conditional probability that given that a student has at least three years of work experience,this student has at least four years of work experience.

P(at least 4 years|the student has at least three years of experience)

[tex]=\dfrac{50/100}{80/100} =\dfrac{5}{8}=0.625[/tex]

The probability that a randomly selected first-year MBA student has at least four years of work experience is 0.5 or 50%.

The question involves the concept of probability in statistics, a part of Mathematics. Here, we are given that there are a total of 100 first-year MBA students. The number of students with at least four years of work experience combines the students with four years and five or more years of work experience. Thus, the students with at least four years of work experience are 15 (four years of work experience) + 35 (five or more years of work experience), which equals 50.

The probability is determined by dividing the number of favorable outcomes by the total number of outcomes. Hence, the probability that a randomly selected first-year MBA student has at least four years of work experience is calculated as 50 (students with at least four years' experience) divided by 100 (total students), which equals 0.5 or 50%.

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Answer: 7:48pm

Step-by-step explanation:

Convert 1h to mins

[tex]1h(\frac{60min}{1h} )=60min[/tex]

add the 38 extra mins.

60+38=98mins

The movie started at 6:10pm, and she has already watched 48 mins of it.

Add 48 to the time and subtract from the length of the movie.

6:10pm + 48 mins=6:58pm (this is the current time)

98-48=50

Let's add 2 mins to make it 7:00pm.

6:58pm+2mins=7:00pm

50-2=48mins

So now it's 7:00pm and we still have 48 mins to watch. Add that to the time.

7:00pm+48mins=7:48pm

Answer:

There is not enough evidence to support the claim that the mean cadmium level in Boletus pinicoloa mushrooms is greater than the​ government's recommended limit (0.5 ppm).

The P-value for this test is P=0.404.

Step-by-step explanation:

The question is incomplete:

The sample size is n=12 and the sample mean is M=6.31/12=0.526 ppm.

This is a hypothesis test for the population mean.

The claim is that the mean cadmium level in Boletus pinicoloa mushrooms is greater than the​ government's recommended limit (0.5 ppm).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=0.5\\\\H_a:\mu> 0.5[/tex]

The significance level is 0.05.

The sample has a size n=12.

The sample mean is M=0.526.

The standard deviation of the population is known and has a value of σ=0.37.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.37}{\sqrt{12}}=0.107[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{0.526-0.5}{0.107}=\dfrac{0.026}{0.107}=0.242[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]P-value=P(z>0.242)=0.404[/tex]

As the P-value (0.404) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean cadmium level in Boletus pinicoloa mushrooms is greater than the​ government's recommended limit (0.5 ppm).

Answer:

2.5 cm

Step-by-step explanation:

The line to the right of the object indicates the diameter. Therefore, the diameter is 5 cm.

The diameter is twice the radius, or

d=2r

We know the diameter is 5, so we can substitute that in for d

5=2r

To solve for r, we need to get r by itself. To do this, divide both sides by 2. This will cancel the 2s on the right.

5/2=2r/2

2.5=r

So, the radius is 2.5 centimeters

Answer:

y = 3

Step-by-step explanation:

y = (3x² + 3x + 6) / (x² + 1)

The power of the numerator and denominator are equal, so as x approaches infinity, y approaches the ratio of the leading coefficients.

y = 3/1

The horizontal asymptote will be;

⇒ y = 3

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The algebraic expression is,

''The horizontal asymptote off of x equals quantity 3 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.''

Now,

We can formulate;

⇒ f (x) = ( 3x² + 3x + 6 ) / (x² + 1)

Hence, We get the horizontal asymptote as;

We know that;

A function f is said to have a horizontal asymptote y = a;

⇒ [tex]\lim_{x \to \infty} f (x) = a[/tex]

So, We get;

⇒ [tex]\lim_{x \to \infty} f (x) = \lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1}[/tex]

⇒ [tex]\lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1} = \lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)}[/tex]

⇒ [tex]\lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)} = 3[/tex]

⇒ y = 3

Thus, The horizontal asymptote will be;

⇒ y = 3

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The z-score for the sample mean in this case is 0.5, which is calculated using the z-score formula, Z = (X - μ) / σ, where X is the sample mean, μ is the population mean, and σ is the standard deviation.

The subject here pertains to the calculation of a z-score, which is a statistical measurement describing a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.

Given the sample mean (56), population mean (50), and standard deviation (12), and the formula for the z-score, which is Z = (X - μ) / σ, we can compute for the z-score as follows:

Substituting these values into the equation, we have: Z = (56 - 50) / 12 = 0.5. Hence, the z-score of the sample mean is 0.5.

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Answer:

$120

Step-by-step explanation:

Area of wall: 12*5=60 square feet

price = 60*2=$120

Answer:

[tex] P(z<-1.55)=0.0606[/tex]

Step-by-step explanation:

For this case we want to find this probability:

[tex] P(z<-1.55)[/tex]

Because they want the area to the left of the value. We need to remember that the normal standard distribution have a mean of 0 and a deviation of 1.

We can use the following excel code: =NORM.DIST(-1.55,0,1,TRUE)

And we got:

[tex] P(z<-1.55)=0.0606[/tex]

The other possibility is use the normal standard table and we got a similar result.

Answer:

Part 1: The statistic

[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)  

And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=35+35-2=68[/tex]  

Replacing we got

[tex]t=\frac{(5135-4436)-0}{\sqrt{\frac{783^2}{35}+\frac{553^2}{35}}}}=4.31[/tex]  

Part 2: P value  

Since is a right tailed test the p value would be:  

[tex]p_v =P(t_{68}>4.31)=0.000022 \approx 0.00002[/tex]  

Comparing the p value we see that is lower compared to the significance level of 0.01 so then we can reject the null hypothesis and we can conclude that the mean for the four year college is significantly higher than the mean for the two year college and then the claim makes sense

Step-by-step explanation:

Data given

[tex]\bar X_{1}=5135[/tex] represent the mean for four year college

[tex]\bar X_{2}=4436[/tex] represent the mean for two year college

[tex]s_{1}=783[/tex] represent the sample standard deviation for four year college

[tex]s_{2}=553[/tex] represent the sample standard deviation two year college

[tex]n_{1}=35[/tex] sample size for the group four year college

[tex]n_{2}=35[/tex] sample size for the group two year college

[tex]\alpha=0.01[/tex] Significance level provided

t would represent the statistic (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the mean enrollment at four-year colleges is higher than at two-year colleges in the United States , the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{1}-\mu_{2}\leq 0[/tex]  

Alternative hypothesis:[tex]\mu_{1} - \mu_{2}> 0[/tex]  

We can assume that the normal distribution is assumed since we have a large sample size for each case n>30. So then the sample mean can be assumed as normally distributed.

Part 1: The statistic

[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)  

And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=35+35-2=68[/tex]  

Replacing we got

[tex]t=\frac{(5135-4436)-0}{\sqrt{\frac{783^2}{35}+\frac{553^2}{35}}}}=4.31[/tex]  

Part 2: P value  

Since is a right tailed test the p value would be:  

[tex]p_v =P(t_{68}>4.31)=0.000022[/tex]  

Comparing the p value we see that is lower compared to the significance level of 0.01 so then we can reject the null hypothesis and we can conclude that the mean for the four year college is significantly higher than the mean for the two year college and then the claim makes sense