Past experience indicates that the time re- quired for high school seniors to complete a standard- ized test is a normal random variable with a standard deviation of 6 minutes. test the hypothesis that = 6 against the alternative that < 6 if a random sample of the test times of 20 high school seniors has a standard deviation s = 4.51. use a 0.05 level of significance.

Past experience indicates that the time re- quired for high school seniors to complete a standard- ized test is a normal random variable with a standard deviation of 6 minutes. test the hypothesis that σ = 6 against the alternative that σ < 6 if a random sample of the test times of 20 high school seniors has a standard deviation s = 4.51. use a 0.05 level of significance.

Answers

Answer 1

At 0.05 level of significance, there is sufficient evidence to support the alternative hypothesis that [tex]\sigma[/tex] < 6.

To test the hypothesis that the standard deviation ([tex]\sigma = 6[/tex] ) against the alternative that ( [tex]\sigma = 6[/tex] ), we can use a chi-square test.

The test statistic for a chi-square test is given by ( [tex]\chi^2 = \frac{(n-1)s2}{\sigma2}[/tex]), where:

The sample size = [tex]n[/tex]

The sample standard deviation = [tex]s[/tex]

The hypothesized standard deviation = [tex]\sigma[/tex]

The sample size, n = 20

The sample standard deviation, s = 4.51

The hypothesized standard deviation, [tex]\sigma[/tex] = 6

Substituting these values into the formula:

[tex][ \chi^2 = \frac{(20-1)(4.51)2}{62} \approx 14.13 ][/tex]

The degrees of freedom for the test is ( n - 1 = 20 - 1 = 19 ).

The test statistic for our chi-square test is ([tex][ \chi^2 = \frac{(20-1)(4.51)2}{62} \approx 14.13 ][/tex] ).

The critical value for a chi-square distribution with 19 degrees of freedom at the 0.05 level of significance is approximately 30.14.

Since our test statistic ([tex]\chi^2 = 14.13[/tex] ) is less than the critical value (30.14), we reject the null hypothesis that [tex]\sigma[/tex] = 6 at the 0.05 level of significance.

Thus, we have sufficient evidence to support the alternative hypothesis that [tex]\sigma[/tex] < 6, suggesting that the standard deviation of the time required for high school seniors to complete the standardized test is less than 6 minutes.

Related Questions

The total cost of a prescription is $119.25. Mr. Jones's co-insurance plan requires him to contribute 15 percent of the cost. What's Mr. Jones's out-of-pocket cost for this prescription?

Answers

Final answer:

To find Mr. Jones's out-of-pocket cost for his prescription, calculate 15% of the total cost of $119.25, resulting in $17.89 after rounding.

Explanation:

The question asks us to calculate Mr. Jones's out-of-pocket cost for his prescription if his co-insurance plan requires him to pay 15% of the total cost. The total cost of the prescription is $119.25.

To find out Mr. Jones's out-of-pocket expense, we calculate 15% of $119.25:

Out-of-pocket cost = 15% of total cost
= 0.15 × $119.25
= $17.8875

So, Mr. Jones's out-of-pocket cost will be $17.8875, which we can round to $17.89 for practical purposes.

One 16-ounce bottle of an energy drink has an average of 400 mg of caffeine with a standard deviation of 20 mg. What is the probability that the average caffeine in a sample of 25 bottles is no more than 395 milligrams?

Answers

That probability is about 10.6%.

[tex] \sqrt[3]{ 3x + 1 - 4 = - 6} [/tex]

Answers

i'm not sure if -6 is out or inside the cubic root but i will solve it for both cases

In case of [tex] \sqrt[3]{3x+1-4} =sqrt[3][-6][/tex] --> (by multiplying the power by 3)
[tex] 3x+1-4 = -6[/tex]
[tex] 3x -3 = -6 [/tex] ---> by adding 3 for the both sides
[tex] 3x = -3 [/tex] ---> by dividing both sides by 3
[tex] x = -1 [/tex]

in case of [tex] \sqrt[3]{3x+1-4} = -6[/tex] ----> we will repeat the first step again
therefore,
[tex] 3x + 1 -4 = (-6)^{3} = -216 [/tex]
[tex] 3x -3 = -216 [/tex] ----> by adding both sides by 3
[tex] 3x = -213 [/tex] ----> by dividing both sides by 3
[tex] x = \frac{-213}{3} = -71 [/tex]
then x = -71
I hope that helps ;)

Use the Change of Base Formula to evaluate log3 58. Then convert log3 58 to a logarithm in base 4. Round to the nearest thousandth.

Answers

[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]
[tex]\log_358=\dfrac{\log_458}{\log_43}\approx\dfrac{2.929}{0.792}\approx3.698[/tex]

HI :) I NEED HELP PLEASE BEFORE 12 AM

Answers

See, please, the solution for the task number 2.

Caleb bought a car for $6,900. He agreed on a five-year loan at a 5.4% interest rate. Calculate what Caleb's monthly payments will be.

Answers

Final answer:

To calculate Caleb's monthly car payments, use the loan amortization formula that deals with compound interest, not simple interest. Input the loan amount of $6,900, the monthly interest rate (annual rate of 5.4% divided by 12), and the total number of payments (5 years times 12 payments per year) into the formula to find the monthly payment.

Explanation:

Caleb's car loan scenario comes under financial mathematics, specifically, it deals with loan amortization using the concept of compound interest. Since the car loan spans multiple years, compound interest is the accurate model to use, not simple interest. As opposed to simple interest which only accrues on the original amount or principal, compound interest accrues on the principal and all interest previously added.

The formula to calculate the monthly payment, P, on a loan is given by, where PV represents t

[tex]P = [r*PV] / [1 - (1 + r)^-n][/tex]

he present value or the amount of loan, which is $6,900 in this case; r is the monthly interest rate which can be calculated as annual interest rate divided by 12, translating to 0.054/12 in this case; and n is the total number of payments (i.e., 5 years of payments with 12 payments per year, hence, 5*12).

To calculate the monthly payment, plug these values into the formula which should give you the monthly payment amount that Caleb needs to pay for his car loan.

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If P(A or B)equals=0.60.6, P(A)equals=0.40.4, and P(A and B)equals=0.350.35, find P(B).

Answers

Answer:

P(B) = 0.55 .

Step-by-step explanation:

We are given that P(A or B) = 0.6 , P(A) = 0.4 , and P(A and B) = 0.35 .

As we know that;

P(A or B) = P(A) + P(B) - P(A and B)

0.6 = 0.4 + P(B) - 0.35

P(B) = 0.35 + 0.6 - 0.4 = 0.55

Therefore, P(B) = 0.55 .

Suppose f(x)=x^2-2. Find the graph of f(5x).

Answers

The function f (x) = x ^ 2 - 2 is given
It is asked to find the graph of f (5x)
So where the x goes we must now place "5x"
In this way the function is as shown below:
f (5x) = (5x)² -2
f (5x) = 25x² -2
The graph of this function is shown in the attached image.

What is the length of the hypotenuse of the triangle?
sides 7cm and 3cm

A. sqrt 20cm
B. sqrt 23cm
C. sqrt 40cm
D. sqrt 58cm

Answers

So use the Pythagorean theorem formula - a² + b² = c²

7² + 3² = c²
49 + 9 = c²
49 + 9 = 58
58 = c²
Sqrt of 58 = 7.6 cm

So the answer is D) Sqrt 58 cm.

Hope this Helps!!

The length of the hypotenuse of the triangle is √58 cm (Option D).

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the sides of the triangle:

Side a = 7 cm (one of the legs)

Side b = 3 cm (the other leg)

Side c = ? (the hypotenuse)

The Pythagorean theorem is:

[tex]c^2 = a^2 + b^2[/tex]

Substitute the given values:

[tex]c^2 = 7^2 + 3^2\\\\c^2 = 49 + 9\\\\c^2 = 58[/tex]

Now, we can find the square root of both sides to solve for c:

c = √58 cm

So, the length of the hypotenuse of the triangle is √58 cm.

The correct answer is: D. √58 cm

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the width of a rectangular picture is 13 in less than the length the area of the picture is 30in 2 what is the length of the picture

Answers

Let x represent the length of the picture. Then its width is represented by (x-13) and its area will be
A = length*width
30 = x(x -13)

This quadratic equation can be put into standard form and factored to find the solutions.
x² -13x -30 = 0
(x -15)(x +2) = 0
x ∈ {15, -2}

A negative length makes no sense, so we conclude ...
the length of the picture is 15 inches.

Answer:
2 would be your length. The exact length would be 2.3
Explanation:
When we multiply using the formula your answer should always add up to 2.3

A round table top has a diameter of 2.6 meters.What is its surface area

Answers

Hello!

To find the area of a circle you use the equation

[tex] \pi r^{2} [/tex]

r is radius which is half the diameter

r = 2.6 / 2

r = 1.3

Put in the values you know

[tex] \pi 1.3^{2} [/tex]

Square the number

[tex]1.69 \pi = 5.31[/tex]

The answer is [tex]1.69 \pi [/tex] or ≈5.31

Hope this helps!

that's just area of a circle

remmber that [tex]A=\pi r^2[/tex] where r=radius and A is area and pi is pi or about 3.14159265

so if diameter is 2.6, ah, tricky, they give you dameter
rmemeber that d/2=r so 2.6/2=d/2=r=1.3

so
[tex]A=\pi r^2[/tex]
[tex]A=\pi (1.3)^2[/tex]
using your calculator
[tex]A=5.309 m^2[/tex]

the surface area is [tex]5.309 m^2[/tex]

a company observes the lifespan of 560 lightbulbs and finds that their data follows a normal distribution. what is the approximate number of light bulbs that fall within two standard deviations from the mean?

Answers

Empirical rule can be used to estimate the number of values that lie with 1, 2 or 3 standard deviations of a Normally distributed population.

According to the empirical rule, 95% of the values lie within 2 standard deviations of the mean.

Total number of bulbs = n = 560
95% of n = 0.95 x 560 = 532

This means, 532 bulbs will lie within 2 standard deviations from the mean

What is the annual rate of productivity advance implied by moore's law? (assume linear growth from the base.) instructions: enter your response rounded to the nearest whole number. %?

Answers

The annual rate of productivity is 34%. Moor's law sates that it i sequal to 34%.

A rectangular dartboard has an area of 648 square centimeters. The triangular part of the dartboard has an area of 162 square centimeters. A dart is randomly thrown at the dartboard. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle?

To the nearest whole percent, the probability is

A) 18
B) 25
C) 35
D) 50

Answers

The answer is B) 25.
Hope this helps!!

Answer: B) 25

Step-by-step explanation:

Given: A rectangular dartboard has an area of 648 square centimeters.

The triangular part of the dartboard has an area of 162 square centimeters.

If a dart is randomly thrown at the dartboard. Assuming the dart lands in the rectangle, the probability (in percent) that it lands inside the triangle will be :

[tex]\dfrac{162}{648}\times100=25\%[/tex]

Hence, the probability that it lands inside the triangle = 25%.

Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 8 inches. How far did Chubby run? Give your answer in terms of pi. (prize is 99 points)

Answers

Answer: 800pi inches

=======================================

Explanation:

The formula to find the circumference of a circle is
C = pi*d
where
C = distance around the circle (aka circumference)
pi = 3.14 approximately
d = diameter

We know that the diameter of the wheel is d = 8, so
C = pi*d
C = pi*8
C = 8pi
is the circumference of the wheel

One full rotation will have the wheel cover a distance of 8pi inches. Imagine that wet paint is on the outer surface of the wheel. If the wheel is rolled out in a straight line, then the wet paint would cover a linear distance of 8pi inches along the flat ground. This is one full rotation, so 100 rotations covers 100*8pi = 800pi inches

Note: if we use pi = 3.14 as the approximation, then the hamster ran approximately 800*pi = 800*3.14 = 2512 inches if the wheel could move

Answer:

6280

Step-by-step explanation:

It's 6280

3/a=9/b-10c solve for a.

Answers

For this case we have the following equation:
3 / a = 9 / b-10c
Rewriting we have:
3 = a * (9 / b-10c)
Clearing to have:
a = 3 / (9 / b-10c)
Answer:
The value of a in terms of variables b and c is given by:
a = 3 / (9 / b-10c)

In a woodworking you are planing boards to make shelves. The planer is set to remove 1/16 inch from a board on each pass the board makes through the planer. If a board starts out at 3/4 inch thick, how many times will you need to send it through the planer to get it down to 5/8 inch?

Answers

Material removed per pass = 1/16 in
Initial thickness = 3/4 in
Final thickness = 5/8 in

If x is the number of passes,
The material removed = (1/16)x in.
Therefore,
3/4 - (1/16)x = 5/8
3/4 - x/16 = 5/8
x/16 = 3/4 - 5/8 = 1/8
x = 16*1/8 = 2

Therefore, the board will be passed through the plane twice.

PLEASE PLEASE HELP WITH THIS

Answers

Since triangles ABC and BCD are similar, we can establish a proportion between the lengths of corresponding sides:
[tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]

We can infer from our picture that [tex]BC=m[/tex]. Also we can find the length of AC by adding AD and CD:
[tex]AC=AD+CD[/tex]
[tex]AC=11+7[/tex]
[tex]AC=18[/tex]

Lets replace the values in our proportion:
[tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]
[tex] \frac{18}{m} = \frac{m}{7} [/tex]
Solving for [tex]m[/tex]:
[tex]m^2=(18)(7)[/tex]
[tex]m^2=126[/tex]
[tex]m= \sqrt{126} [/tex]

We can conclude that the correct answer is: D [tex] \sqrt{126} [/tex]

What is one possible solution for the triangle below?

Answers

Answer:

The correct answer is C, i can promise you that

Step-by-step explanation:

the only one with Angle Z as 94.6 degrees.

One possible solution for the triangle below is:

Option D:

YZ = 95.4

∠X = 26.7°

∠Z = 85.3°

How use law of sines and cosines?

If only one of these is missing, the law of cosines can be used.

3 sides and 1 angle. So if the known properties of a triangle are SSS (side-side-side) or SAS (side-angle-side), then this law applies.

If you want the ratio of the sine of an angle and its inverse to be equal, you can use the law of sine. This can be used if the triangle's known properties are ASA (angle-side-angle) or SAS.

Using Law of sine:

40/sin 68 = 43/sin Z

sin Z = (43/40) * sin 68

sin Z = 0.9967

Z = sin⁻¹0.9967

Z = 85.3°

The only option with the correct value of angle Z is Option D with:

YZ = 95.4

∠X = 26.7°

∠Z = 85.3°

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PLEASE HELP WILL GIVE BRAINLIEST!!!The table below represents the closing prices of stock ABC for the last five days

Answers

Answer:

A. [tex]y=-8.583x+475.215[/tex]

Step-by-step explanation:

We are given,

The table representing the closing prices of stock for the last five days is,

Day Value

1 472.08

2 454.26

3 444.95

4 439.49

5 436.55

Using the linear regression calculator, we have that,

The linear equation that best fits the data is [tex]y=-8.583x+475.215[/tex]

Thus, option A is correct.

hey can you please help me posted picture of question

Answers

The number of roots of a quadratic function can be determined from its discriminant.

If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.

The discriminant can be calculated as:

Disc = b² - 4ac

For the given equation:

Disc = 9 - 4(2)(1) =1

Since the value of discriminant is positive, the function will have two distinct roots.

So, the answer to this question is option B

what is the solution to the system y= 3/4 x - 12 and y = 4x - 31

Answers

For the first one it would be no solution

If the train that Megan is riding covers 80 miles in 2 hours, how fast is the train traveling?

Answers

The train is traveling at 40 mph (miles per hour).

To find this, you divide both 80 and 2 by 2 to find how many miles in a single hour the train travels. Thus giving you 40 miles in an hour (40 mph) as a ginal answer.

I hope this helps!

Final answer:

The average speed of the train Megan is traveling on is 40 miles per hour. It's obtained by dividing the total distance of 80 miles by the total time of 2 hours.

Explanation:

To find the average speed of the train that Megan is riding, which covers 80 miles in 2 hours, we will use the formula for average speed, which is total distance divided by total time. The train travels 40 miles one way and 40 miles back, totaling 80 miles.

Here is the step-by-step calculation:

Calculate the total distance the train travels: 40 miles one way + 40 miles back = 80 miles.

Calculate the total time of the journey: 2 hours.

Divide the total distance by the total time to find the average speed: 80 miles / 2 hours = 40 miles per hour.

This means the average speed of the train is 40 miles per hour.

The graph of a proportional relationship passes through (3, 24) and (1, y). Find y.

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf (\stackrel{x}{3},\stackrel{y}{24})\textit{ we also know that } \begin{cases} x=3\\ y=24 \end{cases}\implies 24=k3\implies \cfrac{24}{3}=k \\\\\\ 8=k\qquad therefore\qquad \boxed{y=8x} \\\\\\ (\stackrel{x}{1},\stackrel{y}{y})\textit{ when x = 1, what is \underline{y}?}\qquad y=8(1)[/tex]

What type of conic section is the following equation? 4x2 + y2 = 36

Answers

The terms are both squares, so it is not a parabola.

The signs of the terms are both positive, so it is a circle or an ellipse.

The coefficients of the terms are different, so it is not a circle, it is an ELLIPSE.

Answer:

Ellipse

Step-by-step explanation:

The signs of the terms are both positive, so it is either a circle or an ellipse.

The coefficients of the terms are different, so it can not be a circle.

Therefore it is an Ellipse.

simplify completely 3x^2+21x-54 over x^2+3x-54

Answers

[tex]\bf \cfrac{3x^2+21x-54}{x^2+3x-54}\implies \cfrac{3(x^2+7x-18)}{x^2+3x-54}\implies \cfrac{3\underline{(x+9)}(x-2)}{\underline{(x+9)}(x-6)} \\\\\\ \cfrac{3(x-2)}{x-6}[/tex]

Answer: 3(x-2) / x-6

Step-by-step explanation: find gcf..

Factor completely the following quadratic expression 16x^2-25y^2

Answers

[tex]16x^2-25y^2 [/tex]

[tex](4x)^2-(5y)^2[/tex]

[tex](4x+5y)(4x-5y)[/tex]

Answer:

(4x+5y)(4x-5y)

Step-by-step explanation:

it is correct i got it right

determine the perimeter of a sector circular AOB whose radius has a length of 4m its central angle is 0.5 rad

Answers

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=4\\ \theta =0.5 \end{cases}\implies A=\cfrac{(4)(0.5)^2}{2}\implies A=0.5[/tex]

which word best describe 8(2x+4)

Answers

Hope it helped you.
~~~~~~~~~~~~~~~~~~

8*2 is 16

Then 8*4 is 32.

Answer is 16x+32

Distribution it should be used 8(2x+4).

-Charlie

The answer you are looking for is A. Coefficient.

A coefficient is a number that is in front of a variable. Examples of this are 6 in 6x, 100 in 100s, and 45 in 45h. Thus making 8 the coefficient of the problem.

There are also no like terms (like 4 and 6 or 5x and 9x), there is no inequality sign (greater than, less than, etc), and there are no constant variables (like 2 and 7 in the equation " 2x - 2 = 7).

I hope this helps!

-7y to the third (4y + y - 3)

Answers

Hello,

So if we have the equation: -7y^3(4y + y - 3), we're essentially distributing "-7y^3" to everything of what's in the parenthesis. When you distribute -7y^3, know that you add exponents but you multiply the numbers. After simplifying you get:

-28y^4 - 7y^4 + 21y^3

**We can still simplify this expression because there are still like terms:

-35y^4 +21y^3

Hope this helps!

May

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