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
Ket [755]
3 years ago
5

Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases: a. Central area 5 .

95, df 5 10 b. Central area 5 .95, df 5 20 c. Central area 5 .99, df 5 20 d. Central area 5 .99, df 5 50 e. Upper-tail area 5 .01, df 5 25 f. Lower-tail area 5 .025, df 5 5
Mathematics
1 answer:
Flauer [41]3 years ago
8 0

Answer:

a) "=T.INV(0.025,10)" and "=T.INV(1-0.025,10)"

And we got t_{\alpha/2}=-2.228 , t_{1-\alpha/2}=2.228

b)  "=T.INV(0.025,20)" and "=T.INV(1-0.025,20)"

And we got t_{\alpha/2}=-2.086 , t_{1-\alpha/2}=2.086

c) "=T.INV(0.005,20)" and "=T.INV(1-0.005,20)"

And we got t_{\alpha/2}=-2.845 , t_{1-\alpha/2}=2.845

d) "=T.INV(0.005,50)" and "=T.INV(1-0.005,50)"

And we got t_{\alpha/2}=-2.678 , t_{1-\alpha/2}=2.678

e) "=T.INV(1-0.01,25)"

And we got t_{\alpha}= 2.485

f) "=T.INV(0.025,5)"

And we got t_{\alpha}= -2.571

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.  

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

We will use excel in order to find the critical values for this case

Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases:

a. Central area =.95, df = 10

For this case we want 0.95 of the are in the middle so then we have 1-0.95 = 0.05 of the area on the tails. And on each tail we will have \alpha/2=0.025.

We can use the following excel codes:

"=T.INV(0.025,10)" and "=T.INV(1-0.025,10)"

And we got t_{\alpha/2}=-2.228 , t_{1-\alpha/2}=2.228

b. Central area =.95, df = 20

For this case we want 0.95 of the are in the middle so then we have 1-0.95 = 0.05 of the area on the tails. And on each tail we will have \alpha/2=0.025.

We can use the following excel codes:

"=T.INV(0.025,20)" and "=T.INV(1-0.025,20)"

And we got t_{\alpha/2}=-2.086 , t_{1-\alpha/2}=2.086

c. Central area =.99, df = 20

 For this case we want 0.99 of the are in the middle so then we have 1-0.99 = 0.01 of the area on the tails. And on each tail we will have \alpha/2=0.005.

We can use the following excel codes:

"=T.INV(0.005,20)" and "=T.INV(1-0.005,20)"

And we got t_{\alpha/2}=-2.845 , t_{1-\alpha/2}=2.845

d. Central area =.99, df = 50

  For this case we want 0.99 of the are in the middle so then we have 1-0.99 = 0.01 of the area on the tails. And on each tail we will have \alpha/2=0.005.

We can use the following excel codes:

"=T.INV(0.005,50)" and "=T.INV(1-0.005,50)"

And we got t_{\alpha/2}=-2.678 , t_{1-\alpha/2}=2.678

e. Upper-tail area =.01, df = 25

For this case we need on the right tail 0.01 of the area and on the left tail we will have 1-0.01 = 0.99 , that means \alpha =0.01

We can use the following excel code:

"=T.INV(1-0.01,25)"

And we got t_{\alpha}= 2.485

f. Lower-tail area =.025, df = 5

For this case we need on the left tail 0.025 of the area and on the right tail we will have 1-0.025 = 0.975 , that means \alpha =0.025

We can use the following excel code:

"=T.INV(0.025,5)"

And we got t_{\alpha}= -2.571

You might be interested in
What are the similarities and differences between the standard form and vertex form of a quadratic equation?
guajiro [1.7K]

Answer and Step-by-step explanation: <u>Standard</u> <u>form</u> of a quadratic equation is expressed as: y=ax²+bx+c, while <u>vertex</u> <u>form</u> is written as:

y=a(x-h)²+k.

The similarities between standard and vertex forms is that they show if the graph of the equation has a <u>minimum</u> (when a>0) or <u>maximum</u> (a<0) and it's easier to determine the y-intercept: for standard, the value of c is the intercept; for vertex, the value k is the intercept.

The advantage of standard form is that you can determine the product and sum of the equation's roots, which is a method to determine them.

The advantages of vertex form are: easier to find the vertex of the graph, which is the pair (h,k) and the axis of symmetry, which is the value of h.

8 0
3 years ago
I DONT KNOW WHAT IS 89090x908
never [62]

Answer:

80 893 720

Step-by-step explanation:

hope dis helps!!!!

6 0
2 years ago
9 of 10
Aleks04 [339]

\frac{3}{10}

Answer:

^^

Step-by-step explanation:

I just pressed 27/90 on the calculator hahahha

6 0
3 years ago
Read 2 more answers
What is 5+3*4-8+2*7 equal to
neonofarm [45]

Answer: 23 is your answer


Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
Multiply the following: show your SOLUTIONS
abruzzese [7]
The answer for the problems are below in the picture let me know if that makes sense.

5 0
3 years ago
Other questions:
  • A company is replacing cables with fiber optic lines in rectangular casing BCDE. If line segment DE = 3 cm and line segment BE =
    12·2 answers
  • Does anybody know how to do this?
    14·1 answer
  • What is PIE multiplied by PIE?
    10·2 answers
  • What is the annual rate for I = $160.67, P = $2000, t = 8 months?
    9·1 answer
  • Water coming out from a fountain is modeled by the function:
    5·2 answers
  • Please helpppppp, i'm stuck
    14·2 answers
  • A hot air balloon holds 3,249 cubic meters of helium. The density of helium is 0.1785 kilograms per cubic meter. How many kilogr
    9·2 answers
  • 875,932,461,160 what digit is in the hundred-millions place of this number.
    10·1 answer
  • The goal of a toy drive is to donate more than 1000 toys. The toy drive already has collected 300 toys. How many more toys does
    12·1 answer
  • You want to make a equation so it would be 5/8 + 2/8
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!