MATHEMATICS COLLEGE

An independent random sample is selected from an approximately normal population with unknown standard deviation. Find the degrees of freedom and the critical t-value for the given sample size and confidence level.(a) n = 6, CL = 90%(b) n = 21, CL = 98%(c) n = 29, CL = 95%(d) n = 12, CL = 99%

Answers

Answer 1

Answer:

(a) For n = 6, CL = 90%,

The degrees of freedom: 5, Critical t-value: 2.571

(b) For n = 21, CL = 98%,

The degrees of freedom: 20, Critical t-value: 2.845

The degrees of freedom: 28, Critical t-value: 2.048

(d) For n = 12, CL = 99%,

The degrees of freedom: 11, Critical t-value: 3.106

Use the concept of critical t- value defined as:

A critical value is a number that is used in hypothesis testing to compare to a test statistic and evaluate whether or not the null hypothesis should be rejected. The null hypothesis cannot be rejected if the test statistic's value is less extreme than the crucial value.

(a) Given that,

n = 6 and a confidence level of 90%,

The degrees of freedom are,

n-1 = 6-1

The degrees of freedom = 5.

To find the critical t-value,

Look it up in the t-distribution table using a confidence level of 90% and a degree of freedom of 5.

From the table,

The critical t-value is approximately 2.571.

(b) Given that,

n = 21 and a confidence level of 98%,

The degrees of freedom are,

n-1 = 21-1

The degrees of freedom = 20.

By referring to the t-distribution table with a confidence level of 98% and degrees of freedom of 20,

The critical t-value is approximately 2.845.

n = 29 and a confidence level of 95%,

The degrees of freedom are,

n-1 = 29-1

The degrees of freedom = 28

Using the t-distribution table with a confidence level of 95% and degrees of freedom of 28,

The critical t-value is approximately 2.048.

(d) Given that,

n = 12 and a confidence level of 99%,

The degrees of freedom are,

n-1 = 12-1

The degrees of freedom = 11

By consulting the t-distribution table with a confidence level of 99% and degrees of freedom of 11,

The critical t-value is approximately 3.106.

To learn more about statistics visit:

brainly.com/question/30765535

#SPJ12

Answer 2

Answer:

Final answer:

To find the degrees of freedom and critical t-value for each given sample size and confidence level, we can use the t-distribution and a t-table. The degrees of freedom (df) for each sample is equal to the sample size minus 1. The critical t-value can be found using the t-table with the corresponding degrees of freedom and the confidence level.

Explanation:

To find the degrees of freedom and critical t-value for each given sample size and confidence level, we can use the t-distribution and a t-table. The degrees of freedom (df) for each sample is equal to the sample size minus 1. For example, for (a) n = 6, df = 6 - 1 = 5. The critical t-value can be found using the t-table with the corresponding degrees of freedom and the confidence level.

For (a) n = 6, CL = 90%, the critical t-value is approximately 1.943.

For (b) n = 21, CL = 98%, the critical t-value is approximately 2.861.

For (c) n = 29, CL = 95%, the critical t-value is approximately 2.045.

For (d) n = 12, CL = 99%, the critical t-value is approximately 3.106.

Learn more about Finding degrees of freedom and critical t-values for given sample sizes and confidence levels here:

brainly.com/question/31236797

#SPJ11

Related Questions

When factoring x2 – 3xy + 2y2 by grouping the first step can be:Question 7 options:x2 – 4xy + xy + 2y2x2 – 2xy – xy + 2y2x2 – 3xy + xy + 2y2x2 + 2xy - 5xy + 2y2
Bruce earns 14.45/h and works 40 hours a week. What is his gross annual income
One number is 10 more than twice another. Their sum is 1. Find the numbers
The width of a rectangle is 10 feet shorter than its length. The area of the rectangle is 60 square feet. Find the length and width. Round your answer to the nearest tenth of a foot.
A population of bacteria is initially 2,000. After three hours the population is 1,000. Assuming this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t).

Write (3y)^2 without exponents

Answers

There are two ways of doing this

3y x 3y
Or
9y

" ^ " indicates exponentiation. " ^2 " indicates squaring, or multiplying the base by itself. Thus, w^2 is the same as w times w.

What is (3y) times (3y)?

Can you help me to do this please?Determine the inverse of the h(x)

Answers

Answer:

$h^(-1)(x)=x^3+6x^2+12x+7$

Explanation:

Given the below function;

$h(x)=\sqrt[3]{x+1}-2$

We'll follow the below steps to determine the inverse of the above function;

Step 1: Replace h(x) with y;

$y=\sqrt[3]{x+1}-2$

Step 2: Switch x and y;

$x=\sqrt[3]{y+1}-2$

Step 3: Solve for y by first adding 2 to both sides;

$\begin{gathered} x+2=\sqrt[3]{y+1}-2+2 \n x+2=\sqrt[3]{y+1} \end{gathered}$

Step 4: Take the cube of both sides;

$\begin{gathered} (x+2)^3=(\sqrt[3]{y+1})^3 \n (x+2)^3=y+1 \end{gathered}$

Step 5: Expand the cube power;

Recall;

$(a+b)^3=a^3+3a^2b+3ab^2+b^3$

Applying the above, we'll have;

$\begin{gathered} (x+2)^3=y+1 \n x^3+3x^2\cdot2+3x\cdot2^2+2^3=y+1 \n x^3+6x^2+12x+8=y+1 \end{gathered}$

Step 6: Subtract 1 from both sides of the equation;

$\begin{gathered} x^3+6x^2+12x+8-1=y+1-1 \n x^3+6x^2+12x+7=y \n \therefore y=x^3+6x^2+12x+7 \end{gathered}$

Step 7: Replace y with h^-1(x);

$h^(-1)(x)=x^3+6x^2+12x+7$

Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.

Answers

Answer:

r = (ab)/(a+b)

Step-by-step explanation:

Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).

Using the Pythagorean theorem, we can write the relation ...

((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2

a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2

-4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab

r = ab/(a+b) . . . . . . . . . divide by the coefficient of r

The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).

_____

The graph in the second attachment shows a trapezoid with the radius calculated as above.

Three baskets weigh 120 pounds how many pounds are 4 baskets

Answers

Answer:

160

Step-by-step explanation:

$(120)/(3) = 40\n40*4 = 160$

Quick!!! I need to do my homework
Solve: x - 1 < 3

Answers

x < 4

given x - 1 < 3 ( add 1 to both sides )

x < 4

or x ∈ ( - ∞, 4 ) ← in interval notation

Find the equation of the line shown

Answers

Answer:

y = x + 1

Step-by-step explanation:

find slope (y2-y1)/(x2-x1)

pick 2 points (0,1) and (1,2)

(2-1)/(1-0) = 1/1 = 1

Since (0,1) you know that y intercept is 1

the equation in slope intercept form: y = x + 1

Other Questions

Central limit theorem Imagine that you are doing an exhaustive study on the children in all of the elementary schools in your school district. You are particularly interested in how much time children spend doing active play on weekends. You find that for this population of 2,431 children, the average number of minutes spent doing active play on weekends is μ = 87.85, with a standard deviation of σ = 118.1. You select a random sample of 25 children of elementary school age in this same school district. In this sample, you find that the average number of minutes the children spend doing active play on weekends is M = 79.07, with a standard deviation of s = 129.91.The difference between M and 1.1 is due to the :_______

Select all the equations where b = 11 is a solution. I need the answer quickly please.

Write the slope-intercept form of the equation of the line2x + 3y = 18

Drag each description to the correct location on the chart. In a large single-elimination basketball tournament, the first round of play begins with 64 teams. In each successive round, the number of teams remaining in the tournament is reduced by half. This relationship can be described by the following exponential function. When this relationship is graphed, determine the quantity and axis that will represent each of the variables. x-axis y-axis Teams Remaining Tournament Round