1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rufina [12.5K]
3 years ago
9

Does going to a private university increase the chance that a student will graduate with student loan debt? A national poll by t

he Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. A researcher wanted to see if there was a significant increase in the proportion of student loan debt for public and nonprofit colleges in 2014. Suppose that the researcher surveyed 1500 graduates of public and nonprofit universities and found that 71% of graduates had student loan debt in 2014. Let p be the proportion of all graduates of public nonprofit universities that graduated with student loan debt. What are the appropriate null and alternative hypotheses for this research question?
A. H0: p = 0.69 Ha: p ≠ 0.69



B. H0: p = 0.69 Ha: p > 0.69



C. H0: p = 0.71 Ha: p ≠ 0.71



D. H0: μ = 0.69 Ha: μ > 0.69
Mathematics
1 answer:
Snowcat [4.5K]3 years ago
5 0

Answer:

Null hypothesis:p \leq 0.69  

Alternative hypothesis:p > 0.69  

Step-by-step explanation:

1) Data given and notation

n=1500 represent the random sample taken

X represent the number of graduates that had student loan debt in 2014

\hat p=0.71 estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

p_o=0.69 is the value that we want to test

\alpha represent the significance level  

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that if there was a significant increase in the proportion of student loan debt for public and nonprofit colleges in 2014 respect to the value of 2013.:  

Null hypothesis:p \leq 0.69  

Alternative hypothesis:p > 0.69  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

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

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.71 -0.69}{\sqrt{\frac{0.69(1-0.69)}{1500}}}=1.675  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed is \alpha=0.05. The next step would be calculate the p value for this test.  

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

p_v =P(Z>1.675)=0.047  

If we compare the p value obtained and using the significance level assumed \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults that said that it is morally wrong to not report all income on tax returns  is not significantly higher than 0.69.  

You might be interested in
What is an equation of the line that passes through the points (4, -6)<br>and (8, -4)
QveST [7]

\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{4}}}\implies \cfrac{-4+6}{4}\implies \cfrac{2}{4}\implies \cfrac{1}{2}

\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y+6=\cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x-8

3 0
3 years ago
Read 2 more answers
Find the value of c so that the polynomial p is divisible by (x+2)
alexandr1967 [171]

Answer:

The value of c is 8.

Step-by-step explanation:

When a function is divisible by a factor, it will get 0 value. So, you have to substitute x = -2 into p(x) and equals to 0 :

p(x) = 4 {x}^{3}  + c {x}^{2}  + x + 2

p( - 2) = 4 {( - 2)}^{3}  + c {( - 2)}^{2}  + ( - 2) + 2

4( - 8) + 4c - 2 + 2 = 0

- 32 + 4c = 0

4c = 32

c = 32 \div 4

c = 8

3 0
3 years ago
Put the following steps in order for multi step equations
kakasveta [241]

Soil is the thin layer of material covering the earth's surface and is formed from the weathering of rocks. It is made up mainly of mineral particles, organic materials, air, water and living organisms—all of which interact slowly yet constantly. ... Therefore, most living things on land depend on soil for their existence.

5 0
3 years ago
In his bank account, Jean-Paul has a balance of $0.00
GenaCL600 [577]
Well JP has $0.00 in his bank account which means his has more debt

Albert has $11.10 which means he has greater absolute value.

5 0
3 years ago
Read 2 more answers
340 students went to the first dance but only 306 went to the second. What is the percent decrease in the attendance from the fi
Bond [772]
First find the difference that went by subtracting the 2 numbers:

340 - 306 = 34

 divide that by the number of students that went to the first dance:

34 / 340 = 0.1 = 10% decrease

8 0
3 years ago
Read 2 more answers
Other questions:
  • How many teaspoons are in a quart
    7·1 answer
  • there are 1012 souvenir paperweights that need to be packed in boxes each box will hold 12 paperweights how many boxes will be n
    9·1 answer
  • the length of a rectangle is 6in.more than than its width .Its area is 50 sq.in Find the width of the rectangle....
    10·1 answer
  • There are 2255 female students in SMK Setia Alam. If these number of student represent 55%of all students, calculate the total n
    9·1 answer
  • To increase an amount by 3% what single multiplier would you use?
    8·1 answer
  • If (x/3)-1 is twice as large as (x/4)-3, what is the value of x?
    11·2 answers
  • Bobby describes two lines to Frank, telling him that beginning at point A, line #1 goes up 3 units and to the right 8 units, whi
    5·1 answer
  • Pls help im confused with this
    11·1 answer
  • Please I need help thank you in advance ​
    14·2 answers
  • Phil is going to purchase a home with a sale price of $225,000. He is able to put 20% down for her down-payment and get a mortga
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!