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1 year ago

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UCF is a major Metropolitan University located in Orlando Florida. UCF is advertising their bachelor in Economics with the stati

stic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13). The Director of Institutional Research at UCF is interested in testing this information. She decides to conduct a survey of 50 randomly selected recent graduate economic students. The sample mean is $43,350 and the sample standard deviation is 15,000. Alpha =0.05
Using the given Null Hypothesis and level of significance
A. The null hypotheisis should not be rejected
B. Not enough information is given to answer this question.
C. I have no idea
D. The null hypotheisis should be rejected D Question 34

1 answer:

adoni [48]1 year ago

7 0

Answer:

D. The null hypotheisis should be rejected

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the starting salary of a graduate with a bachelor in economics significantly differs from $48,500.

Then, the null and alternative hypothesis are:

$H_0: \mu=48500\\\\H_a:\mu\neq 48500$

The significance level is 0.05.

The sample has a size n=50.

The sample mean is M=43350.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=15000.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{15000}{\sqrt{50}}=2121.32$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{43350-48500}{2121.32}=\dfrac{-5150}{2121.32}=-2.43$

The degrees of freedom for this sample size are:

$df=n-1=50-1=49$

This test is a two-tailed test, with 49 degrees of freedom and t=-2.43, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=2\cdot P(t$

As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the starting salary of a graduate with a bachelor in economics significantly differs from $48,500.

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Sitting at the edge of a cliff, you throw a stone vertically upward with a velocity of 30 m/s. The height of the stone above the

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Step-by-step explanation:

Given that,

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And it's initial velocity is 30m/s

u=30m/s

Using calculation

Let find it turning point

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Then, f'(t) =3-t

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So, 0=3-t

Then t=3secs

So let know the inflection point to show if t=3secs is the maximum point or minimum point

Then, we need second integral of f(t)

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Since f''(t) is negative this shows that the point is the maximum point

So at t=3secs is the maximum point,

So now to know the maximum point

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t=3secs

f(t)=3(3)-0.5(3)²

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Since f(t) is in 10m units

Then,

The height is f(t) =10×4.5

f(t) =45m

Then the maximum height of the stone is 45m and the time to reach the maximum height is t=3secs

Now, Using equation of motion

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v=u-gt. Upward motion g=9.81m/s2

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0=30-9.81t

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t=-30/-9.81

t=3.06secs

t=3.1secs. To 1d.p

If we have used g=10m/s², it will have the same value as the graph and the maximum and minimum point calculation

Maximum height, using equation of motion

v²=u²-2gH

0²=30²-2×9.81H

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Then,

H=-30²/-19.62

H=45.87

a. From the graph it shows that the maximum value of the is 4.5m at time t=3secs

b. Now, the maximum height of stone as shown on the graph is 4.5m

And since is 10 meter unit scale

Then the height becomes 4.5×10

Maximum height is 45m.

c. The stone will spend two times the time it uses to reach t maximum height to return to the height of the cliff

Time to return back to the cliff is

T=2t

T=2×3

T=6secs

d. If the stone hits the ground after t=7secs

So after the ball reached a maximum height of 45m, he has spent 3secs, so we can calculate the distance the stone travelled from the maximum to the ground

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S=78.48m

So the total distance from the maximum height down to the bottom of the cliff is 78.48m

Then, the height of the cliff is the height from the maximum height to the bottom of the cliff minus the maximum height reach by the stone

Then,

H(cliff)=78.48-45.87

H(cliff)=33.48m

From the graph

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Answer:

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