Under what circumstances is a t statistic used instead of a z score for a hypothesis test

Answers

Answer 1

If you know the population standard deviation sigma, then you'd use the z score. Otherwise, you would use a t statistic. However, if n is large enough (usually n > 30), then you can approximate the T distribution with the normal Z distribution. Some stats textbooks will allow the use of a z score if n > 30. Though it will depend on your specific book and/or your teacher.

Related Questions

What is the area of this figure?

Answers

As stated by @mathmate, the figure can be split into two rectangles (see picture). Then, we can find the total area by adding the areas of the individual rectangles. The area of the first rectangle is calculated by multiplying its length times width:

6 * 5 = 30

The area of the second rectangle is calculated by multiplying its length and width:

12 * 4 = 48

Now, we can add the areas to find the total area of the figure:

30 + 48 = 78

The figure's area is 78 cm².

How many hours minutes and seconds are in 2165 days?

Answers

there is 24 hours in a day

2165 days x 24 hours = 51,960 total hours

there are 60 minutes per hour

51,960 x 60 = 3,117,600 total minutes

there are 60 seconds per minute

3,117,600 x 60 = 187,056,000 total seconds

Let , 4 ,− 7 be a point on the terminal side of θ . find the exact values of cos θ , csc θ , and tan θ .

Answers

Ok, you are given a point and you need to find the exact values for [tex]cos \theta csc \theta & tan \theta[/tex]

First thing first. We need to see if we are working with a unit circle and find the radius.

How to tell if we are working with a unit circle?
We know [tex]x^2 + y^2 = r^2[/tex] is a circle.

We know that to find the radius we can use the following formula:
[tex]r^2 = \sqrt{x^2 + y^2}[/tex]

If [tex]r^2 = \sqrt{x^2 + y^2} = 1[/tex] we are working with a unit circle.

Lets see if it = 1.
[tex]r^2 = \sqrt{4^2 + -7^2}[/tex]
[tex]r^2 = \sqrt{16 + 49}[/tex]
[tex]r^2 = \sqrt{65}[/tex]

Square both sides now
[tex]\sqrt{r^2} = \sqrt{\sqrt{65}}[/tex]
[tex]r = \pm 65^{\frac{1}{4}}}[/tex]

Since we squared, we have a + and a - but we disregard the - because we do not have - radii
[tex]r = 65^{\frac{1}{4}}}[/tex]
We can also say
[tex]r = \sqrt[4]{65}[/tex]

Ok, since r does not equal 1, we are not working with a unit circle but we have found r, which is our radius.

Now that we know the value of r, which is [tex]r = 65^{\frac{1}{4}}}[/tex], we need to look at the identities of cos, csc and tan.

The identities:
[tex]cos \theta = \frac{x}{r}[/tex]
[tex]csc \theta = \frac{1}{y}[/tex]
[tex]tan \theta = \frac{y}{x}[/tex]

Now that we know their identities and know the radius of our circle, we can find the exact values of cos, csc and tan.

[tex]cos \theta = \frac{x}{r} = \frac{4}{65^{\frac{1}{4}}}[/tex]
[tex]csc \theta = \frac{1}{y} = \frac{1}{-7}[/tex]
[tex]tan \theta = \frac{y}{x} = \frac{-7}{4}[/tex]

The exact values for cos, csc and tan given the point (4,-7) are:
[tex]cos \theta = \frac{4}{65^{\frac{1}{4}}}[/tex]
[tex]csc \theta = \frac{1}{-7}[/tex]
[tex]tan \theta = \frac{-7}{4}[/tex]

The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.

Let be a Point of the form [tex](x,y)[/tex] that is the Terminal Side of angle [tex]\theta[/tex], in sexagesimal degrees. By Trigonometry, we know that the Cosine, Cosecant and Tangent of the Angle are, respectively:

[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (1)

[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex] (2)

[tex]\tan \theta = \frac{y}{x}[/tex] (3)

If we know that [tex]x = 4[/tex] and [tex]y = -7[/tex], then the exact value of all the trigonometric relations are:

[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex]

[tex]\cos \theta = \frac{4}{\sqrt{4^{2}+(-7)^{2}}}[/tex]

[tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex]

[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex]

[tex]\csc\theta = \frac{\sqrt{4^{2}+(-7)^{2}}}{4}[/tex]

[tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex]

[tex]\tan \theta = \frac{y}{x}[/tex]

[tex]\tan \theta = -\frac{7}{4}[/tex]

The exact values are [tex]\cos \theta = \frac{4\sqrt{65}}{65}[/tex], [tex]\csc \theta = \frac{\sqrt{65}}{4}[/tex] and [tex]\tan \theta = -\frac{7}{4}[/tex], respectively.

Please see the related question for further details: https://brainly.com/question/15225546

a game has a deck of cards with 10 red cards, 4 blue cards, and 2 yellow cards. you randomly choose two cards(choose one and choose the second one without replacement) find the probability of choosing a blue card and a yellow card

Answers

[tex] \displaystyle
|\Omega|=\binom{16}{2}=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\
|A|=4\cdot2=8\\\\
P(A)=\dfrac{8}{120}=\dfrac{1}{15}\approx7\% [/tex]

four friends share 3 fruits bars equally how much does each friend get

Answers

3/4 = 0.75

each friend gets 0.75 of a bar

They each would get 3/4

A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given: 50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 The following histogram is a representation of the data. Calculate the median ages

Answers

What you have to do to find the median of the data is first put that data into order numerically. You can go largest to smallest or smallest to largest, it doesn't matter.

22, 24, 28, 28, 30, 31, 31, 32, 32, 35, 36, 37, 38, 41, 42, 42, 44, 44, 45, 46, 46, 47, 47, 49, 50

Once you put them into order, you count towards the middle. You have 25 data points, so the middle, which will be your median number, will be 13 points in.

The median is 38

Final answer:

The median age of the sales representatives is 37.5 years.

Explanation:

To find the median ages of the sales representatives, we first need to order the ages in ascending order:

22 24 28 28 30 31 31 32 32 35 36 37 38 41 42 42 44 44 45 46 47 47 49 50 56

Since there are 25 data values, the middle value will be the median age. To find the middle value, we divide the number of data values by 2, which gives us 12.5. Since the median is the average of the two middle values, we can take the average of the 12th and 13th values in our ordered list:

Median age = (37 + 38) / 2 = 37.5 years

A plane left on time at noon on Monday. It arrived at its destination at 8:16PM the same day, which was 16 minutes late. On average, how many seconds did the plane fall behind every fifteen minutes?

Answers

The plane arrived on 8:16 pm and was 16 minutes late. This means the arrival time of plan was 8:00 pm. The plane left on noon i.e. 12:00 pm.

So total expected time of the journey was = 8 hours

8 hours means 8 x 60 minutes = 480 minutes

480 minutes can also be seen as 32 groups of 15 minutes each as 15 x 32 = 480.

In 32 groups of 15 minutes each the plane was late by a total of 16 minutes.

So, in every 15 minute the plane was late by 16/32 minute = 0.5 minute

Thus, we can conclude that on average the plane fall behind 0.5 minutes in every 15 minutes

To find the average delay per fifteen-minute interval, convert the total delay of 16 minutes into seconds, then divide by the number of fifteen-minute intervals between noon and 8:00 PM, yielding an average delay of 30 seconds per interval.

The question asks us to calculate how much time the plane fell behind schedule, on average, every fifteen minutes. Since the plane arrived 16 minutes late, we first need to convert this delay into seconds: 16 minutes is equal to 960 seconds (16 minutes imes 60 seconds/minute). To calculate the plane's average delay per fifteen-minute interval, we divide the total delay in seconds by the total number of fifteen-minute intervals between noon and the expected arrival time at 8:00 PM, which is 32 intervals (8 hours ×4 intervals/hour). Therefore, the average delay per interval is 960 seconds \/ 32 intervals = 30 seconds per interval.

The sides of a rectangle are in the ratio of 4:5. If the width is 28 in., find the length, the perimeter, and the area of this rectangle.

Answers

If the width is 28 inches, then divide that by 4 and you get 7. You multiply that by 5 to get the length. That would be 35. Just to check, you know that the width 28 and length 35 are in ratio 4:5 if you divide by 7. The perimeter would be 2(35+28)=63*2=126. So the perimeter is 126. The area would be 35*28 which is 980. To sum up, the answers are as follows.

Length: 35 in
Perimeter: 126 in
Area: 980 inches squared.

SCIENCE HELP 10 POINTS!!!!!

The greenhouse effect traps heat near earth's surface. Greenhouse gases in the atmosphere—carbon dioxide, water vapor, methane, and nitrous oxide—allow the shorter waves of ultraviolet radiation from the sun to enter earth's lower atmosphere. However, these gases do not allow the longer wavelengths of infrared radiation to pass back out to the outer atmosphere. The result is that the lower atmosphere heats up.This result happens naturally, but it can be accelerated by human activities. Since the late 1800s, human activity has greatly altered the amount of greenhouse gases that enter the atmosphere. Burning fossil fuels, farming, and clearing forests, as well as industry, have all contributed to increases of carbon dioxide (CO2), methane, nitrous oxide, and other greenhouse gases in the atmosphere.The result is that temperatures in the troposphere have gone up. Many scientists identify this increase in greenhouse gas emissions as contributing directly to global warming. This suggests that human activity has had an impact on the global climate.

The author argues that in modern times, the greenhouse effect *

A.helps keep the Earth warm

B.has increased because of human activity

C.is in a natural cycle of changing

D.has changed local weather patterns

Answers

D it is changing local weather patterns

C.is in a natural cycle of changing

Which figure shows how a shape can be rotated about an axis to form the given object?

Answers

The answer is as shown in the attachment which is the first diagram (on the left) on the second row which is highlighted in the attachment

That is the only figure which when rotated about the axis will form a cylindrical form as required.

The top two will form into a solid sphere and the last would form into a solid cylinder and not the one as required.

Answer:

Option C.

Step-by-step explanation:

In this question we will go by every option.

Option A). When a circle showing in the figure is rotated then a hollow ring will be formed.

Option B). In this option when a circle like structure with two layers is rotated about an axis it will forms a ring with two layers. Inner part of the ring will be empty.

Option C). In this option when a vertical strip is rotated by the axis, it will form the cylinder similar to the object shown in the figure.

Option D). In this option when a strip attached to the axis is rotated, a sold cylinder is formed.

Therefore Option C. is the correct option.

If the graph of the function h is defined by = h(x)+x^2+9 is translated vertically downward by 9 units, it becomes the graph of a function g. Find the expression for
gx

Answers

The answer is g(x) = x².
Solution:
The graph of h(x) = x²+9 translated vertically downward by 9 units means that each point (x, h(x)) is shifted onto the point (x, h(x) - 9), that is,
(x, h(x)) → (x, h(x) - 9)
The translated graph that represents the function is defined by the expression for g(x):
g(x) = h(x) - 9 = x² + 9 - 9 = x²

h(x) = x²+9 → g(x) = x² shows that the graph of the equation g(x) = x² moves the graph of h(x) = x²+9 down nine units.

A soccer ball is kicked from the ground in an arc defined by the function, h(x) = -2x 2 + 8x. At what point does the ball hit the ground?

Answers

check the picture below. That's about what a parabola for an "initial velocity" case would look like.

anyhow, it hits the ground at two points, when it began, and when it came back down, and that happens when y = 0.

[tex]\bf h(x)=-2x^2+8x\implies \stackrel{h(x)}{0}=-2x^2+8x\implies 0=-2x(x-4)\\\\ -------------------------------\\\\ 0=-2x\implies 0=x\qquad \impliedby \textit{when it began}\\\\ -------------------------------\\\\ 0=x-4\implies \boxed{4=x}\qquad \impliedby \textit{when it came back down}[/tex]

Answer:

4 seconds

Step-by-step explanation:

h(t) = -3t^2 + 12t

0 = -3t^2 + 12t

0 = -3t(t - 4)

0 = t - 4

t = 4

Therefore, it takes 4 seconds for the rocket to hit the ground.

hope it helps :)

mark brainliest!

Suppose that 5 green balls and 12 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn?

Answers

If the first ball is replaced and that we are not concern about the color of the first ball, then there is no concern for the first ball at all.

Total number of balls = 5 + 12 = 17
Total number of purple balls = 12

P(second one is purple) = 12/17

Answer: 12/17

Uisng the concept of probability, the probability that the second ball drawn is purple is 12/17

Given the Parameters :

Number of green balls = 5 Number of purple balls = 12

Total number of balls = 12 + 5 = 17

Recall :

Probability = required outcome / Total possible outcomes

Since selection is made with replacement :

P(purple) = number of purple balls / total number of balls

P(purple) = 12/17

Therefore, the probability of drawing a purple ball is 12/17

Learn more : https://brainly.com/question/18796573

a piece of baseboard is 2/3 yard long. Angela cuts the board into pieces that are 1/6 yard long. How many pieces are there

Answers

namely, how many times does 1/6 go into 2/3, well

[tex]\bf \cfrac{\quad \frac{2}{3}\quad }{\frac{1}{6}}\implies \cfrac{2}{3}\cdot \cfrac{6}{1}\implies \cfrac{2}{1}\cdot \cfrac{2}{1}\implies 4[/tex]

A test is worth 50 points. Multiple-choice questions are worth 1 point, and short-answer questions are worth 3 points. If the test has 20 questions, how many multiple-choice questions are there?
A. t for test, q for questions
B. m for multiple choice, s for short answer
C. s for short answer, t for test
D. p for points, m for multiple choice

apex mcr

Answers

Use the following formula to find the answer to this question:

S * Q + M * Q = P

Representations:

S = The amount of points for short-answer questions.

M = The amount of points for multiple-choice questions.

Q = Number of questions for each of the type of questions that add up to the total number of questions on the test (20 questions).

P = Total points on the test.

Since there is a total of 50 points on the 20 question test, you would need to divide up the amount of questions there are for each of the type there are on the test, short-answer, and multiple-choice.

3 * Q + 1 * Q = P

Now find how many of the type of questions there are out of 20 questions on the test that would add up to the total number of points on the test.

3 * Q + 1 * Q = 50

(15 + 5 = 20 questions on the test, 15 and 5 can be used for the number of questions for each type of question on the test).

3 * 15 + 1 * 5 = 50

45 + 5 = 50

50 = 50

So, your total number of multiple choice questions are: 5.
And, your total number of short answer questions are: 15.

I would go with D. for your answer. I may be wrong.

I hope this helps.

~ Notorious Sovereign

There are 12 people having lunch.Each person wants 1/3 of a sub sandwich.How many whole sub sandwiches are needed ?use models to show answer.

Answers

12 people * (1/3 sandwich per person) = 4 sandwiches

3 and 2/3. 4 if the looking for a whole number

What is the equation for the graph shown below?

Answers

Try this way:
the common view of the required equation is y=(x-a)(x-b), where 'a' and 'b' are the interception points (the curve and Ox).
using the coordinates of interception points it is possible to make up the required equation: x=3 and x=5.
y=(x-3)(x-5).
If to check the equation using the coordinates of the vertex (4;-1):
-1=(4-3)(4-5) ⇔ -1=-1, it means, that the equation made up is correct.

answer: y=(x-3)(x-5) or y=x²-8x+15.

What is the degree measure of angle A?_____ degrees

Answers

Hello!

Vertical angles are congruent

Angle A is vertical angles to the angle that measures 80

The answer is 80

Hope this helps!

A rancher has 300 feet of fencing to enclose a pasture bordered on one side by a river. the river side of the pasture needs no fence. find the dimensions of the pasture that will produce a pasture with a maximum area.

Answers

I think your best answer is a pasture that is 75 feet by 150 feet, which will give you 11,250 sq ft of pasture

A jar contains 8 large red marbles, 5 small red marbles, 7 large blue marbles, and 4 small blue marbles. if a marble is chosen at random, which of the conditional probabilities is larger, p(red|large) or p(large|red)?

Answers

8 large red, 5 small red, 7 large blue, 4 small blue:

totally = 24 marbles

P(red)= 13/24

let A red and B large

P(A/B)= P(A∩B)/P(B)

P(B)= 15/24 =.625

P(A∩B)= 8/24 = .333

P(A/B) =.333/.625 =.533

P(B/A) =.625/.333= 1.875

so the probability of p(large/red) is larger.

find the length of the side f .

Answers

I am pretty sure the answer is 10. Someone correct me if I'm wrong
[tex]10 {}^{2} + 15 {}^{2} = 18 {}^{2} \\ 100 + 225 = 325 \\ \sqrt{325} = 18 [/tex]

The length of side "f" would be about 9.95.

Using Pythagorean Theorem, you have the hypotenuse or side "c" (18) which is longest side. You also have side "b" (15).
Since the equation is "a^2 + b^2 = c^2”, fill in for "b" and "c" giving "a^2 + 15^2 = 18^2"
Solve for "a". Square each known value, leaving "a^2 + 225 = 324". Subtract 225 from each side, leaving "a^2 = 99" then use the square root on each side. Thus getting "a = 9.94987..., which rounded up is 9.95.

I hope this helps!

The beginning balance in Cash was $3,500. Additional cash of $2,000 was received. Checks were written totaling $2,500. The cash balance is Question 3 options: $2,000. $6,000. $4,500. $3,000.

Answers

3500+2000 = $5500
5500-2500 = $3000 so it would be 3000

the answer is. $3000

If events A and B are mutually exclusive, find P(A/B)
A. P(A)
B. 1
C. 0
D. P(A)/P(B)

Answers

I'm assuming you're asked to find [tex]\mathbb P(A\mid B)[/tex], not [tex]\mathbb P\left(\dfrac AB\right)[/tex] (which is nonsense as far as I can tell).

By definition,

[tex]\mathbb P(A\mid B)=\dfrac{\mathbb P(A\cap B)}{\mathbb P(B)[/tex]

We're told the two events are mutually exclusive, which means their intersection is disjoint and the probability of their intersection is 0. So the answer is C.

14 m equals how many mm

Answers

14 m is 14000 mm..........

14 m is 14000 mm the conversion calculator says it all, good luck :-)
xoxo-Sky

CC=\frac{5}{9}(F - 32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.

A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

A temperature increase of
5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only
B) II only
C) III only
D) I and II only

Answers

The answer would be D I and II only

My work:
The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III is true

The answer would be D! Hope this helped you out.

"you want to buy a new sports car from roy's cars for $51,800. the contract is in the form of a 48-month annuity due at a 9.2 percent apr. what will your monthly payment be"

Answers

the answer would be $1,284.13

Answer: $1,284.13

Step-by-step explanation:

use the Pythagorean theorem to determine if a triangle with sides lengths 2 feet 4 ft 5 ft is a right triangle

Answers

So, here's the equation to determine this:
2^2 + 4^2 = 5^2
Multiply:
4 + 16 = 25
20 = 25
This is not true.
This is not a right triangle

Which of the following is the correct simplification of 7•4²÷ 8 -12

Answers

The answer you are looking for would be 2.

This can be found by solving with PEMDAS. First, you do the 4^2 (4*4), which equals 16. Next, you multiply 16 by 7, to get 112. Then, you'd divide 112 by 8. This gives you 14. Finally, subtract 12 from 14 to get your final answer of 2.

I hope this helps!

I’m not sure but I tried working it out and I got 2.26272819199.. so it should be 2

A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water in simplest form?

Answers

The ratio of cleaner to water will be given by:
cleaner:water
1 1/2:12
simplifying the above we get:
3/2:12
multiplying both sides by 2 we get:
2×3/2:12×2
3:24
hence the answer is 3:24

Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.4 seconds. suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is less than 8.4 seconds. what would you use for the alternative hypothesis?

Answers

9seconds!!!!!!!!!!!!!!!!!!!

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