In: Statistics and Probability

**The value of a college degree is greater than it has
been in nearly half a century, a least when compared to the
prospect of not getting a degree (www.pewresearch.org, January 28,
2014). Due to this fact, more and more people are obtaining college
degrees, despite the soaring costs. The accompanying table shows
the proportions of college degrees awarded in 2010 by colleges and
universities, categorized by a graduate's race and
ethnicity.**

**The race and ethnicity of 500 recent graduates are
recorded and shown in the last column of the table.**

Race/Ethnicity | 2010 Proportions | Recent Numbers |

White | 0.73 | 350 |

Black | 0.10 | 50 |

Hispanic | 0.09 | 60 |

Asian | 0.08 | 40 |

**At the 5% significance level, test if the proportions have
changed since 2010.**

The expected frequency for each category here is computed as:

proportion of category*500 because 500 is total frequency here.

The chi square test statistic value here is computed as:

Race |
2010
Proportion |
O_i |
E_i |
(O_i -
E_i)^2/E_i |

White | 0.73 | 350 | 365 | 0.616438356 |

Black | 0.1 | 50 | 50 | 0 |

Hispanic | 0.09 | 60 | 45 | 5 |

Asian | 0.08 | 40 | 40 | 0 |

5.616438356 |

From the above table, last column, we get the required test statistic value here as:

Degrees of freedom = n - 1 = 3

Therefore the p-value here is computed from the chi square distribution tables as:

As the p-value here is 0.13 > 0.05 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence to reject the claim that the proportions are like the 2010 today as well.

A researcher claims that 86% of college graduates say their
college degree has been a good investment. In a random sample of
1000 graduates, 845 say their college degree has been a good
investment. At a = 0.10, is there enough evidence to reject the
researcher’s claim? (Adapted from Pew Research Center)

1. You should invest in a professional degree if:
a. Your post-degree income is greater than your income before
earning the degree
b. The present value of the incremental benefits is greater
than the present value of the incremental costs
c. The degree increases the present value of your human
capital
d. You can get into an Ivy League School
2. The price a well-informed investor would pay for an asset
in a free and competitive market is called the:...

Prince has graduated from college and has been working nearly 1
year now, earning $45,000 for a firm. She expects to remain at the
firm another few years. She lives at home still to save money, has
$5,000 in credit card debt, $10,000 in student loans, $1,500 in
savings beyond her usual checking account balance. She likes eating
out and going to clubs on weekends. What challenges does Prince
face budgeting for herself and setting priorities? Discuss.

Suppose f(x) is a rational function in which the degree of the
numerator is greater than the degree of the denominator. To
integrate f(x), the first step is
a) Factor the denominator into distinct linear factors
b) Factor the numerator into distinct linear factors
c) Polynomial long division
d) Make a rationalizing substitution
e) None of the above

Why is the future value of annuity due always greater than the
future value of an ordinary annuity assuming everything equals
2?
Why the present value of an annuity due is always greater that
than the future value of an ordinary annuity assuming everything
else equals?

It has been determined that an x-ray machine has a Half Value
Layer of 1.80 mm Aluminum. Explain the concerns with the emission
of the photon beam and patient exposure. What are the changes to
the continuous and discrete spectrums, and the correction measures
required? Be descriptive and do not use fragmented sentences.

Supply is elastic whenever the value of the elasticity of supply
is positive and greater than 1.
a) True
b) False
The price elasticity of supply is calculated as the change in
supply divided by the change in price.
a) True
b) False
If the income elasticity for canned food is 0.8, then canned
food is an inferior good.
a) True
b) False
The demand for heating oil in the short run is more elastic than
the long run demand...

2. As long as the interest rate is greater than zero, the
present value of a single sum will always:
Select one:
a. Equal the future value if the time period is one year.
b. Increase as the interest rate increases.
c. Be more than the future value.
d. Increase as the number of periods decreases.
e. Decrease as the number of periods increases.
3.
A project costs $525 and has cash flows of $100 for the first
three years...

Consider the
probability that greater than 8888 out of 151151 people have not
been in a car accident. Assume the probability that a given person
has not been in a car accident is 57%57%.
Approximate the
probability using the normal distribution. Round your answer to
four decimal places.

Consider the probability that greater than 99 out of 157 people
have not been in a car accident. Assume the probability that a
given person has not been in a car accident is 55%.
Approximate the probability using the normal distribution. Round
your answer to four decimal places.

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