K L M
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
K
L
M
![Mean - 8953
Standard Deviation 3273.46
According to the College Board's website, the average tuition cost per year for a public four-year
college (in-state cost) is $10,230.
A) Assume that you disagree with the claim. Do you think the average tuition cost is higher?
Or lower?
E) Using a significance level a = 0.05, find the critical value using the following steps.
1. What are the degrees of freedom?
Average tuition cost is higher than $10230.
B) Using your answer in part A, write a set of hypotheses (null hypothesis and alternative
othesis) to represent that claim and its complement. Replace the ?s below with the
appropriate inequality signs (<,<>,2). Highlight the hypothesis that represents your
claim.
d.f.= n- 1
(1)Here the sample size is 20 , we know degrees of freedom = n - 1 =
20 -1 =19
Ho:u? $10,230
Ha:p=10230 Hi:p>10230
2. Will this be a one-tailed or two tailed test?
Ha:u?$10,230
A right-tailed test (one-tailed), for which a t-test for one mean will be used.
C) Gather data for tuition cost of 20 different universities. Assume the data you gather is
normally distributed.
3. Using table 5 from the back of your textbook (page A18 in Appendix B), what is
the critical value?
How to Create your data set:
Informåtion provided, the significance level is a=0.05\alpha = 0.05, and the critical
value for a right-tailed test is te=1.729
Follow the directions to fill in the table below with 20 college's tuition costs.
• Navigate to https://www.collegetuitioncompare.com/compare/tables/
in the drop down menus, ONLY select School Type as "Public School" and School
Level as 4 year or higher." Leave the rest of the drop down menus as is. Then select
"update."
Scroll down to the bottom of the list and for "Number of schools to show," select "All."
The list given will be in alphabetical order. You will be selecting 20 college tuition
costs from this list. Do NOT just use the first 20 entries or even 20 consecutive
entries. You will need to randomly select 20 entries from the entire list. Try to make
sure you have a good range of tuition costs as well.
• Write the tuition cost from the first column, "Tuition & Fees/In-State" for that college
in the table below.
F) Add the critical values to the graph below and shade the rejection region.
(Special Instruction: For this part, it is recommended that you do this by hand. You can print
out this page and use the image below as a template to write on or you can create a handwritten
normal curve. Take a photo of your graph and replace the image below with it. If you need any
technical assistance with this process.
Since it is observed that t--1.745St=1.729t=-1.745 le t ce=1.729, it is then
concluded that the null hypothesis is not rejected.
3565
7290
7409
11068
Using the P-value approach: The p-value is p-0.9514p = 0.9514, and
since p=0.951420.05p= 0.9514 \ge 0.05, it is concluded that the null hypothesis is not
rejected.
%3D
10299
8315
3950
9672
%3D
14924
10958
7396
6946
6834
11108
14812
11068
8273
10904
3120
11149
D) Calculate the mean and standard deviation of your data set. You may use technology such
as Google Sheets, Excel, or a T-83/TI-84. Round to the nearest hundredth.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f12ad35-0575-421d-9d22-a9955b17e4ef%2Feba3bd76-aebf-47d6-82a7-56d47c9a040f%2Fn0qapcg_processed.jpeg&w=3840&q=75)
![T-Test Results: tstats =-1.745, p-value 0.9514
I) What is the P-value? View the video Hypothesis Testing for the Mean (Siqma Unknown)
Part II to learn how to use Google Sheets to calculate the P-value of a t-test (transcript
for Hypothesis Testing for the Mean (Siqma Unknown) Part II video).
40
30
p- value = 0.9514
J) Make a decision to reject or fail to reject the null hypothesis using either the test
statistic or the P-value. Note that the same conclusion will be reached using either
method.
20
Don't reject Ho
0.20
0.05
K) Interpret the decision in the context of the original claim.
0.00
40 35 3.0 25 20 15 10 -0.5 0.0 0.5 10 15 20 25 3.0 3.5 40
G) Calculate the test statistic. Replace the ?s in the formula with the appropriate values.
Round to the nearest hundredth.
L) If you lower the level of significance to a = 0.01, does your decision change? Explain
your reasoning.
ミー
ナこ815310230
3273.46
こ - 12.77
731.97
M) Describe the type I and type Il errors that could occur in our test by completing each of
the following statements.
: .745
(type I, type I) error will occur when the actual mean of college
(at most, at least) $10,230 but you reject the null
tuition cost is
t = ?
hypothesis, Ho: µ? $10,230.
H) Add the test statistic to your graph from part F, and insert the image below.
(type I, type Il) error will occur when the actual mean of college
(less than, greater than) $10,230 but you fail to
• A
tuition cost is
reject the null hypothesis, Ho: u ? $10,230.
$דר1 <
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to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f12ad35-0575-421d-9d22-a9955b17e4ef%2Feba3bd76-aebf-47d6-82a7-56d47c9a040f%2Fx0guc0a_processed.jpeg&w=3840&q=75)
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