Explain why the​ t-distribution has less spread as the number of degrees of freedom increases. Choose the correct answer below. A. The​ t-distribution has less spread as the degrees of freedom increase because the variability introduced into the​ t-statistic becomes greater as n increases. B. The​ t-distribution has less spread as the degrees of freedom increase​ because, as n​ increases, s becomes closer to by the law of large numbers. C. The​ t-distribution has less spread as the degrees of freedom increase​ because, as n​ increases, less information is known about by the law of large numbers. D. The​ t-distribution has less spread as the degrees of freedom increase​ because, for large values of​ n, n​30, the​ t-distribution and the normal distribution are the same.

Answers

Answer 1

Answer:

B. The​ t-distribution has less spread as the degrees of freedom increase​ because, as n​ increases, s becomes closer to sigma by the law of large numbers.

Step-by-step explanation:

The sample standard deviation, s gets considerably closer to the population standard deviation, σ, this trend follows the proposition of the law of large numbers whereby the mean or average value changes as the sample size, n increases. According to the law of large numbers, as the sample size increases, the sample mean gets continously closer to the population mean, sample standard deviation follows this same trend and thus variability or spread decreases as sample size increases.

Answer 2

The plausible reason that explains why the t-distribution will have a less spread as the number of degrees of freedom increases is because: as n​ increases, s becomes closer to by the law of large numbers. (Option B)

Note the following:

Based on the theorem of large number, the population mean and sample mean will get closer as the sample size increases.By implication, the sample standard deviation, s, and the population standard deviation, σ becomes closer too, thus, the spread will reduce as the sample size increases.

Therefore, the plausible reason that explains why the t-distribution will have a less spread as the number of degrees of freedom increases is because: as n​ increases, s becomes closer to by the law of large numbers. (Option B)

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Related Questions

Given the following equations, determine the relationship of the lines they represent: y = 5 and x = 6.

Answers

Answer:

2x2/er5

Step-by-step explanation:

2x2/Ed would be the answer

Which images below are scalene triangles?

Triangle A has three sides each measuring 7 units. Triangle B has two sides that are equal in length, and the base is longer than the two sides. Triangle C has no sides of equal length. Triangle D has sides of length seven, three, and six.
Triangles A and D
Triangles B and D
Triangles A and C
Triangles C and D

Answers

Answer:

Triangle C and D

Is your correct answer

Triangle A have 3 sides equal so it is equilateral triangle

Triangle B have 2 sides equal so it is isosceles triangle

Triangle C have no equal sides so it is scalene triangle

Triangle D have no equal sides so it is scalene triangle

Triangles C and D are scalene triangles.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle A has three sides each measuring 7 units.

Triangle B has two sides that are equal in length, and the base is longer than the two sides.

Triangle C has no sides of equal length.

Triangle D has sides of length seven, three, and six.

Now, We know that;

A scalene triangle have different sides.

Hence, Triangles C and D are scalene triangles.

Thus, We get;

Triangles C and D are scalene triangles.

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Help me solve for x. 16^x = x^2​

Answers

Hello! Let’s begin, But before that, I hope you can mark me as the brainliest, just a hope.


x * 2^4x = x^2

2^4x = x

I’m afraid you can’t simplify more, but it could be

2^2x/2 = root x

you could solve for it yourself, because the other guy is not likely to answer.

Who’s smart at math?

Answers

Answer:

a

Step-by-step explanation:

times 4

Answer:

C. 35 to 49 Minutes

Step-by-step explanation:

For a $150.000 mortgage with an interest rate of 5.5% paid over 20 years, the monthly payment is $1,031.83. After one
month, what is the balance of the loan?
Round your answer to the nearest dollar
Do NOT round until you calculate the final answer.

Answers

Answer: 149656

Step-by-step explanation:

The  balance of the loan is $148,968

Using this formula

Loan balance=Mortgage amount-Monthly payment

Where:

Mortgage amount=$150.000

Monthly payment=$1,031.83

Let plug in the formula

Loan balance=$150.000-$1,031.83

Loan balance=$148,968

Inconclusion The  balance of the loan is $148,968

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A school had decided to hire a new vice principal. A recent issue 4 of the NEA magazine stated that the average vice principal salary s for a school of similar size is $60,000. At the request of the Board of Education, the principal conducts his own survey of vice principal's salaries. His survey of 25 schools revealed an average salary or $72,000 and a standard deviation of $9,000. Perform a hypothesis test at a 5% significance level to test the magazine's claim.

Required:
a. What is the appropriate sampling distribution to use?
b. State the null and alternative hypotheses.
c. State the decision rule at a significance level of 5% show all calculations
d. Illustrate all key numbers and areas on a graph.
e. What decision should the school principal make?
f. What type of error can possibly be made with the decision in part (e)?
g. What is the value of the Maximum Tolerable Error for this problem?

Answers

Answer:

1.) t - distribution

2.) H0 : μ = 60000 ; H1 : μ > 60000

3.) P < α (Reject Null) ; P > α (fail to reject Null)

4.) Reject H0

Type 1 error

Step-by-step explanation:

Null hypothesis, H0 : μ = 60000

Alternative hypothesis, H1 : μ > 60000

Decison rule at 5% significance ;

P < α (Reject Null)

P > α (fail to reject Null)

Xbar = 72000 ; std = 9000

Test statistic :

(Xbar - μ) ÷ (std / sqrt(n))

(72000 - 60000) ÷ (9000 / sqrt(25))

12000 ÷ 1800

Test statistic = 6.667

Using the Pvalue calculator from test statistic :

Test statistic = 6.667 ; df = 24 - 1 = 24

Pvalue = 0.00001

Pvalue < α ; Hence, we reject the Null

Type 2 error : This means accepting a Null hypothesis that should be rejected.

Allison is looking to buy a new car but has low credit score. Which of the following statements is FALSE?

Answers

The option that is false regarding the low credit score is that she is more likely to get a loan with a low-interest rate.

What is a credit score?

A credit score is a numerical expression that is based on a level analysis of a person's credit files, to represent the creditworthiness of an individual.

In this case, she is not likely to get a loan with a low-interest rate because of her poor credit score.

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Please help asap!!!!

Answers

Answer:

[tex] m\widehat {MP} =46\degree [/tex]

Step-by-step explanation:

By inscribed angle theorem:

[tex] m\angle MQP=\frac{1}{2} \times \widehat {MP} [/tex]

[tex] 23\degree =\frac{1}{2} \times m\widehat {MP} [/tex]

[tex] 23\degree \times 2= m\widehat {MP} [/tex]

[tex] m\widehat {MP} =46\degree [/tex]

what value of x will make the faction equivent 3/5=x/36

Answers

Answer:

x = 21.6

Step-by-step explanation:

Solution by Cross Multiplication

For the equation

35=x36

The cross product is

3×36=5×x

Solving for x

x=3×365

and reducing

x=21.6

Solution by Proportion

Since the equation is an equality

If

36 ÷ 5 = 7.2

Then it is true that

x ÷ 3 = 7.2

Solving for x

x = 3 × 7.2

x = 21.6

The area of an ellipse with axes of length
2a and 2b is ab.
The percent change in the area when a increases by
2.74% and b increases by 2.65% is

Answers

Answer:

The area increases by 5.46261%

Step-by-step explanation:

Well firstly, the area of an ellipse is not ab, but it's proportional to ab ([tex]\pi ab[/tex] where a and b are the semi-minor and semi-major axes).

This tells us that when a increases by 2.74% and b increases by 2.65% the new area will be:

[tex]A = \pi \cdot (a \cdot 102.74\%)(b \cdot 102.65\%) = \pi a b \cdot 102.74\% \cdot 102.65\% = \pi ab \cdot 105.46261\%[/tex]

The percentage change in area of the ellipse is 5.5%

The area of an ellipse with an axes of length  of 2a and 2b is πab.

Area of ellipse = πab

Since a increases by  2.74%, hence a = (100% + 2.74%)a = 1.0274a

Also, b increases by  2.65%, hence b = (100% + 2.65%)b = 1.0265b

Therefore the new area = π * 1.0274a * 1.0265b = 1.055πab

The ratio in the area = 1.055πab/ πab = 1.055

The percentage change in area of the ellipse is 5.5%

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Trying to understand this, someone help pls thank you !

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Lines.

We know that perpendicular lines have a inverse negative slope, such that

m1*m2 = -1

hence, m1 = -1/m2

so the perpendicular line is,

==> y-(5) = 3/2(x-(-6))

==> y+5 = 3/2(x+6)

==> y+5 = 3/2*(x) +9

=> y = 3/2(x) +9-5

==> y = 3/2*(x) + 4

hence the correct option is D.)

I'm a brainy plus member that shows it doesn't expire until 3/2022, but when I take a picture and click on answer it won't give the answer to me. It is blurry. Please let me know what is wrong.

Answers

Answer:

Can I see it actually?

Step-by-step explanation:

Abduls average speed is 40 mph in heavy traffic and his average speed is 50 mph in light traffic if he was in heavy traffic 1 hour and light traffic for 3 hours how far did Abdul travel

A. 90

B. 270

C. 190

D. 55​

Answers

Answer:

c

Step-by-step explanation:

1 hour in heavy traffic = 40 miles

3 hours in light traffic = 50*3 = 150 miles

150+40 = 190 miles travelled

i need help w this plz thanks

Answers

Answer:

x = 4√7

y = 8√7

Step-by-step explanation:

Reference angle = 60°

Opposite = 4√21

Hypotenuse = y

Adjacent = x

To find x, apply TOA

Tan 60 = Opp/Adj

Tan 60 = (4√21)/x

x * Tan 60 = 4√21

x = (4√21)/Tan 60

x = (4√21)/√3 (tan 60 = √3)

Rationalize

x = (4√21*√3)/√3*√3

x = (4√63)/3

x = (4*3√7)/3

x = 4√7

To find y, apply SOH:

Sin 60 = Opp/Hyp

Sin 60 = (4√21)/y

y*Sin 60 = 4√21

y = 4√21/sin 60

y = (4√21)/(√3/2)

y = ✓(4√21 × 2/√3)

y = (8√21)/√3

y = 8√7

This is due today! Please answer this:

Answers

Answer:

1. - 6.75

2. 15/28

3. - 3.3

Step-by-step explanation:

The first is correct because a positive times a negative is a negative.

The second is incorrect. It should be 15/28 because a negative times a negative is a positive.

The third is incorrect because a positive times a negative is a negative.

The answer should be

1. - 6.75

2. 15/28

3. - 3.3

HELP ME THIS IS MISSING HOMEWORK AND I DONT WANT ANY FILES OK!!!!!!!!!!!!!!!!!

Answers

Answer:

4a) [tex]\frac{2}{3}[/tex] · (5 + 7)

b) 3 ÷ (3/5)

c) ([tex]\frac{2}{3}[/tex] - [tex]\frac{1}{2}[/tex]) ÷ 3

Step-by-step explanation:

PLEASE HELP FAST GEOMERTY

Answers

Answer:

26

Step-by-step explanation:

125+29=154

180-154=26

26 is your answer. Good luck.

The two figures are similar. Find the ratios
(red to blue) of the perimeters and of the
areas. Write the ratios as fractions in
simplest form.

(100 points)

Answers

Answer:

1/5 to 1/5

Step-by-step explanation:

Consider the expression - 63 - |-74 +25 a. Estimate the value of the expression. Show your work. SOLUTION​

Answers

Answer:

-137-l+25a

Step-by-step explanation:

The given expression is :

- 63 - |-74 +25 a

We need to find the value of the expression.

Gere, l and a are variables.

-63-74 = -137

So,

= -137-l+25a

Hence, the value of the expression is equal to -137-l+25a

Megan's text messaging plan costs $5 for the first 700 messages and 30¢ for each additional text message. If she owes $63.20 for text messaging in the month of January, how many text messages did she send that month?

Answers

Answer:

Fixed cost $14 -350 messages

variable $ 0.25 each message i think

Step-by-step explanation:

63.20-5.00=58.20
58.20/.30=194
So she sent 700+194 for a total of 894 texts

how to get the answer.
how to get the 1.2762815625?
I know it says to multiple, but how to multiple to get that number?
thanks

Answers

9514 1404 393

Answer:

  1.05 × 1.05 × 1.05 × 1.05 × 1.05 = 1.2762815625

Step-by-step explanation:

An exponent indicates how many times the base is a factor in the product. That is, 1.05 to the 5th power means ...

  1.05⁵ = 1.05 × 1.05 × 1.05 × 1.05 × 1.05

This multiplication expression is evaluated in the usual way.

  = 1.1025 × 1.05 × 1.05 × 1.05

  = 1.157625 × 1.05 × 1.05

  = 1.21550625 × 1.05

  = 1.2762815625

__

All scientific and graphing calculators have a button for computing the power of a number. On my calculator its label is [tex]\displaystyle \boxed{y^x}[/tex]. The particulars of the function of this button can be found in the manual for your calculator.

For on-line calculators, such as the go.ogle calculator, or the Desmos graphing calculator, the caret (^) is used to signify an exponent. (See the input line in the first attachment for an example.)

how to solve:

-25/j = 5

Answers

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: -5

Explanation:

First -25/j = 5

-25 = 5j

-25/5 = 5j / 5

-5 = j

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

5x+4y=12. 3x + 6y=8. Help me plaeaee

Answers

Answer:

x = - 20 / 3, y = 14 / 3

Step-by-step explanation:

In the picture

Which box of crackers is a better deal?
190 grams - $1.49
850 grams - $6.99
Explain your thinking.​

Answers

Answer:

Since each cracker in the 190 gram box costs $ 0.0078 while the 850 gram box costs $ 0.0082 each, the 190 gram box is a better deal.

Step-by-step explanation:

Knowing that a 190-gram box of crackers costs $ 1.49 and an 850-gram box costs $ 6.99, to determine which of them is a better deal, the following calculation must be performed:

1.49 / 190 = 0.0078

6.99 / 850 = 0.0082

Therefore, since each cracker in the 190 gram box costs $ 0.0078 while the 850 gram box costs $ 0.0082 each, the 190 gram box is a better deal.

I have 2 congruent, parallel, rectangular bases.

Answers

Answer:

The 3D figure formed is a Cuboid.

Answer:

The figure with 2 congruent, parallel, rectangular bases is a cuboid.

Write the equation for the function g(x), which can be described as a
vertical shift 13 units up from the function f(x) = In x –1

Answers

Answer:

Step-by-step explanation:

When you shift up or down, the function gets added to or subtracted from the expression on the right of the y value.  Put in simpler language, for this question, the equation becomes.

g(x) = f(x) + 13

And the solution is

g(x) = ln(x) - 1 + 13

g(x) = ln(x) + 12

Jana is making a model of a coke can in her math class. The actual height of the coke can is 4.83 inches. If she is using a scale of 1 cm is equal to 0.3 inches, how many cm tall is her model?

A 161 cm
с 16.1 cm
B 1.61 cm
D 1.449 cm​

Answers

Answer:

D

Step-by-step explanation:

Find the mean of the data in the bar chart below.

Answers

Answer:

10.5

Step-by-step explanation:

Mean = average so 18+4+12+8/4 = 10.5

Answer:

10.5

its on khan academy i double checked

The median of the set of data with values 10,12,15,16,18,20 is?​

Answers

The median of the set of data with values 10,12,15,16,18,20 is 15.5.

What is the median?

The median is one of the measures of central tendency.

The median is the middle value of a data set.

When the data set is even, the median is found by adding the two middle values and dividing by 2.

Data and Calculations:

10,12,15,16,18,20

Total value = 91

Median = 15.5 (15 + 16)/2

Thus, the median of the set of data with values 10,12,15,16,18,20 is 15.5.

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What is the slope of 4x-2y=6

Answers

Answer:

slope= -2

Step-by-step explanation:

Slope is -2
See work up in photo below. Good luck.
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