A data set includes data from student evaluations of courses. The summary statistics are n=89​, x=3.44​, s=0.67. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative​ hypotheses?
A.
H0​: μ=3.50
H1​: μ>3.50
B.
H0​: μ=3.50
H1​: μ<3.50
C.
H0​: μ≠3.50
H1​: μ=3.50
D.
H0​: μ=3.50
H1​: μ≠
(I also need the test statistic and p-value) thank you so much in advance :)

Answers

Answer 1

We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0

The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.

We go with answer choice D to form the null and alternative hypotheses.

The sign ≠ in the alternative hypothesis tell us that we have a two tail test.

---------------------------------------

Let's compute the test statistic

z = (xbar - mu)/(s/sqrt(n))

z = (3.44 - 3.50)/(0.67/sqrt(89))

z = -0.84483413122896

z = -0.84

The test statistic is roughly -0.84

---------------------------------------

Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.

Use a calculator or a Z table to determine that

P(Z < -0.84) = 0.2005

which is approximate

Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401

The p-value is roughly 0.401

-----------------------------------------

Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.

The conclusion based on that means that μ=3.50  must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50


Related Questions

where are parabolas on your hand?

Answers

parabolas are there on my hand palms and it must be there on your hands too but why are you asking this question?

PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)


–6



3



–59



26

Answers

Answer:

1st option

Step-by-step explanation:

Evaluate f(- 5) then substitute the value obtained into g(x)

f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then

g(3) = - 4(3) + 6 = - 12 + 6 = - 6

4 pounds of oranges costs $ 12 . What is the unit price per pound?

Answers

3 dollars per pound....

Answer:

3 dollars per pound

Step-by-step explanation:

Unit Price = Cost / Pounds of oranges

Unit Price = 12 / 4

Unit Price = 3

The unit price per pound is $3

PLEASE ANSWER

The distance from the vertex of the curve to the focus is equal to _____.

Here’s the options

the distance from the vertex to the directrix

the distance from the vertex to the y-axis

the distance from the vertex to the origin

a constant

Answers

Answer:

The distance from the vertex to the directrix.

Step-by-step explanation:

According to this question, we are speaking about a parabola, which has the characteristic that the distance from the vertex to the focus is equal to the least distance from the vertex to the directrix.

Hence, the right answer is: The distance from the vertex to the directrix.

When printing an article of 2400 words, an entrepreneur decides to use two sizes of letters, using the largest one a printed page contains 1200 words. Using the smallest, the page contains 1500 words the article must occupy 17 full pages in the magazine how many pages must be printed using small letters?

Answers

Step-by-step explanation:

x= Number of small pages

y= Number of full pages

1 x + 1 y = 21 .............1

Total words

1200 x + 1500 y = 27000 .............2

Eliminate y

multiply (1)by -1500

Multiply (2) by 1

-1500 x -1500 y = -31500

1200 x + 1500 y = 27000

Add the two equations

-300 x = -4500

/ -300

x = 15

plug value of x in (1)

1 x + 1 y = 21

15 + y = 21

y = 21 -15

y = 6

y = 6

x= 15 Number of small pages

y= 6 Number of full pages

Which number shows four hundredths
.004 .04 .400 4.00

Answers

Answer:

hello the answer is .04/0.04

Answer:

.04 is four hundredths

Step-by-step explanation:

I hope this helps

Assume that x and y are both differentiable functions of t. Find dx/dt when x=11 and dy/dt=-4 for the equation xy=99 .

Answers

Differentiating both sides of

xy = 99

with respect to t yields

x dy/dt + y dx/dt = 0

When x = 11, we have

11y = 99   ==>   y = 9

and we're given that dy/dt = -4 at this point, which means

11 (-4) + 9 dx/dt = 0   ==>   dx/dt = 44/9

Area of rectangle or triangle

Answers

Answer:

48 cm²

Step-by-step explanation:

shaded area = area of rectangle - area of triangle

area of rectangle = 7 × 8 = 56 cm²

area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 7 - 3 = 4 cm and h = 8 - 4 = 4 cm

area of triangle = [tex]\frac{1}{2}[/tex] × 4 × 4 = 2 × 4 = 8 cm²

Then

shaded area = 56 - 8 = 48 cm²

một công ty kinh doanh 1 loại sản phẩm có
- Đơn giá bán là 20.000 đồng
- Định phs là 150.000 đồng khi mức tiêu thụ nhỏ hơn 30.000 sản phẩm
- Biến phí đơn vị là 10.000 đồng
y/ cầu:
a. Hãy xác định tỷ lệ biến phí và tỷ lệ đảm phí?
b. Hãy xác định điểm hòa vốn?
c. Công ty sẽ lời hoặc lỗ tại mức tiêu thụ là 12.000 sản phẩm? 17.000 sản phẩm?
d. Độ lớn đòn bẩy kinh doanh của cty là bao nhiêu tại mwucs tiêu thục là 12.000 snar phẩm? 17.000 sản phẩm ? Nêu ý nghĩa của các con số đó
e. Nếu giá bán tăng lên 25.000 đ/sp và biến phí tăng lên 17.000 đ/sp thid điểm hòa vốn của cty sẽ như thế nào

Answers

Answer:

ask in English then I can help u

Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol? The answer is an EXPRESSION, not an actual answer!! WILL MARK BRAINLIST!!!

Answers

Answer:

see below

Step-by-step explanation:

amount of water w

l liter of pure alcohol = 100% alcohol

solution is 45 % percent alcohol

total amount of fluid is w+l

(w+l)( .45) = l*.100

Distribute

.45w  + .45 l = 1l

.45 w = 1l - .45l

.45 w = .55l

w = .55l / .45

w =11/9 l

Kofi is 3 years older than Ama.If Ama is now x years old, what is kofi age​

Answers

Answer:

x+3

Step-by-step explanation:

Kofi is 3 years older than Ama, so the answer is "x+3".

t "To Do" list has four items: 1) Organize email folders 2) Create a schedule for next month 3) Help a coworker and 4) Answer a customer inquiry. Which item should you probably do first ? a) Answer a customer inquiry b) Organize email folders c) Help a coworker d) Create a schedule for next month

Answers

Answer:

I think A) Answer a customer inquiry

Step-by-step explanation:

Because customers come first

find the missing segment below brainly

Answers

Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{6}{4}=\dfrac{x}{20-x}[/tex]

[tex]\\ \sf\longmapsto 6(20-x)=4x[/tex]

[tex]\\ \sf\longmapsto 120-6x=4x[/tex]

[tex]\\ \sf\longmapsto 120=6x+4x[/tex]

[tex]\\ \sf\longmapsto 120=10x[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{120}{10}[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

(b) If 124n= 232 five, find n.

Answers

Answer:[tex]n=\frac{58}{31}[/tex]

Step-by-step explanation:

[tex]124n=232\\\frac{124n}{124}=\frac{232}{124}\\n=\frac{232}{124}=\frac{58}{31}[/tex]

The value of n is 18.75. To find the value of n, we need to solve the equation: 124n = 232 five

Let's first convert "232 five" into a numerical value:

"232 five" means 2325 (since five is in the units place).

Now, the equation becomes:

124n = 2325

To solve for n, divide both sides of the equation by 124:

n = 2325 / 124

Now, perform the division:

n = 18.75

So, the value of n is 18.75.

To know more about equation:

https://brainly.com/question/10724260

#SPJ2

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 60 cookies. The mean is 22.36 and the standard deviation is2.97 . Construct a ​80% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.

Answers

Answer:

2.665 < σ < 3.379

Step-by-step explanation:

Given :

s = 2.97

Sample size, n = 60

α = 80%

χ² Critical value (two - tailed), df = (60-1) = 59

χ² = 45.577 ; χ² = 73.279

The 80% confidence interval for the standard deviation :

s * √(n - 1) / χ² critical

2.97 * √(60 - 1) / 73.279 < σ < 2.97 * √(60 - 1) / 45.577

2.665 < σ < 3.379

Which of the following could NOT be the value of a correlation coefficient?
Select one:
a. 0.98
b.-0.76
c. -1.00
d. 1.34

Answers

Answer:

1.34 cannot be a correlation coefficient

Step-by-step explanation:

The correlation coefficient must be between (and can include) -1 to 1

1.34 is not  between -1 and 1

A pond contains 33 fish. Two are caught, tagged, and released back into the pond. After the tagged fish have had a chance to mingle with the others, eight fish are caught and released, one at a time. Assume that every fish in the pond is equally likely to be caught each time, regardless of which fish have been caught (and released) previously (this is not a realistic assumption for real fish in a real pond). The chance that among the fish caught in the second stage (after the tagging), at least four and at most eight were previously tagged is__________.

Answers

Answer:

0.2424

Step-by-step explanation:

Total number of fish = 33

Total number of tagged fish = 2

Each fish has equal probability of being caught (remember that the focus is on the second stage of fish selection) and that probability is 1/33 = 0.0303

- When the question says at least 4 and at most 8 are tagged fish, it means that 4/8 or 1/2 or half of the fish selected were tagged fish. This gives us the figure to use in computation.

- So first of all, the probability that a fish caught is a tagged fish is (1/33) x 2

which is = 0.0303 x 2  =  0.0606

Now if 8 fish were caught and we want to know the probability that at least half of the eight fish (which is 4 fish) were tagged fish, what do we do?

- Multiply the probability of picking a tagged fish by 4; since each fish is replaced before the next selection.

0.0606 x 4  =  0.2424

Find the length of BC

Answers

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine or tangent.

Remember: SOH-CAH-TOA

Looking from the given angle, we want to find the opposite side and we know the hypotenuse. Therefore, we should use sine.

sin(51) = BC / 58

BC = 58 x sin(51)

BC = 45.1 units

Hope this helps!

Step-by-step explanation:

Hey there!

From the above given figure;

Angle CAB = 51°

AB = 58

Taking Angle CAB as reference angle we get;

Perpendicular (p) = BC= ?

Hypotenuse (h) = 58

Now;

Taking the ratio of sin we get;

[tex] \sin( \alpha ) = \frac{p}{h} [/tex]

[tex] \sin(51) = \frac{bc}{58} [/tex]

Simplify it;

0.7771459*58 = BC

Therefore, BC = 45.0744.

Hope it helps!

Find the integer pair that has the given product and sum. The product is 28 The sum is 11​

Answers

Answer:

7 and 4

Step-by-step explanation:

when you multiply 7×4 the answer is 28 and when you add them the answer is 11.

I hope this helps

Answer:

4 and 7

Step-by-step explanation:

xy = 28 ..........1

x + y = 11........2

x = 11 - y.........3

substitute 3 in 1:

(11 - y)*y = 28

-y² + 11y - 28 = 0

y² - 11y + 28 = 0

( y - 7)( y - 4) = 0

y = 7 or y = 4

subs in 2:

x = 4 or x = 7

pairs: (4 ; 7) and (7 ; 4)

Relate what you know about simplifying expressions to what you know about
factoring. For example, before you can factor 12x + 20y + y, you need to simplify it.
Explain why.

Answers

Because there is y since they are the same alphabetical letters they can be added such that 12x+21y.

In a group of 50 students, 12 play basketball and volleyball
, 9 play volleyball
and soccer, 8 play basketball and play soccer, and 4 play all 3 sports.
Altogether, 21 play basketball, 22 play volleyball, and 19 play soccer. How
many of the 50 students don't play any of the 3 sports?

Answers

Answer:

17 don't play any

Step-by-step explanation:

12+9+8+4=33

33-50=17

represent - 8,5 - 2 on a number line​

Answers

Answer:

I hope this helps

you have to.first draw a number line and mark where the given numbers are

I NEED HELP PLEASE AND THANK YOU!!! ASAP

Answers

Answer:

71

Step-by-step explanation:

Initial angle lies in 4th quadrant

Answer: 71 Initial line sets in 4th Quadrant

Please help do in an hour

Answers

Answer:

-4

Step-by-step explanation:

a1 = -8

an = an-1 +2

a2 = a1+2 = -8+2 = -6

a3 = a2+2 = -6+2 = -4

A local rental car agency has 200 cars. The rental rate for the winter months is 60%. Find the probability that in a given winter month fewer than 140 cars will be rented. Use the normal distribution to approximate the binomial distribution.

Answers

Answer:

[tex]P(Z\leq2.89)=0.9981[/tex]

Step-by-step explanation:

Sample size [tex]n=200[/tex]

Rental Rate [tex]R=60\%[/tex]

Probability =(P<140)

Generally the equation for mean of distribution is mathematically given by

[tex]\mu=nR\\\\\mu=200*0.60\\\\\mu=120[/tex]

Generally the equation for Standard deviation of distribution is mathematically given by

[tex]\sigma=\sqrt{npq}[/tex]

[tex]\sigma=\sqrt{200*0.60*0.40}[/tex]

[tex]\sigma=6.9[/tex]

Therefore

Z-score for x=140 is

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{140-120}{6.9}[/tex]

[tex]Z=2.89[/tex]

From table

[tex]P(Z\leq2.89)=0.9981[/tex]

Find the measure of the incanted angle to the nearest degree

Answers

Answer:

Sinx = 21/40

x = inverse of sin (21/40)

x= 31.6682

hope u got it

Answer:

31.6 degrees

Step-by-step explanation:

sin-¹(p/h) = 31.6

Find the area of the sector round your answer to the nearest 10th

Answers

9514 1404 393

Answer:

  398.2 cm²

Step-by-step explanation:

The area of the whole circle is ...

  A = πr²

  A = π(13 cm)² = 169π cm²

The 270°  sector is 3/4 of the whole circle, so its area is ...

  sector area = (3/4)(169π cm²) ≈ 398.2 cm²

Use the Unit Circle to find the exact value of the trig function. Cos(45)

1/2
√2/2
√3/-2
1

Answers

In a unit circle a line reaching from origin to the circle's circumference specifies the trigonometric functions.

A point where the line which comes from origin to the circumference intersecting it has coordinates [tex](\cos\theta,\sin\theta)[/tex].

In our case [tex]\theta=45^\circ[/tex] which lifts the line up by 45 degrees and makes it intersect circumference at [tex](\cos45^\circ,\sin45^\circ)[/tex].

In the upper right quadrant the angle between x and y axis is 90 degrees so a line coming in at angle of 45 degrees would split the quadrant in half, that means sine and cosine 45 degrees will be equal.

As you may noticed a point has coordinates cos, sin which means the distance between 0 and y coordinate where the point on a circle is, is called [tex]\cos\theta=\cos45^\circ[/tex].

Because cosine 45 degrees is so simple in interpretation it has a known value of [tex]\cos45^\circ=\sin45^\circ=\frac{\sqrt{2}}{2}[/tex].

Hope this helps :)

Which of the following is NOT a requirement for testing a claim about two population standard deviations or​ variances? A. The populations are independent. B. One of the populations is normally distributed. C. The two samples are simple random samples. D. This test requires that both populations have normal distributions.

Answers

Answer:

B. One of the populations is normally distributed.

Step-by-step explanation:

To test a claim about two population standard deviation or variance, it is imperative that the data meets certain requirements which include :

Randomness : Data must not be biased as such it must be drawn as a random sample from a larger group.

The data must be independent. That is not related to one another, the outcome of one should not rely on the outcome or value of another.

Both groups must be drawn From a population which is normally distributed.

One group being normally distributed by stribuyed while the other isn't a requirement for hypothesis testing in this scenario.

I want to know how to solve this equation

Answers

Answer:

one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.

The answer would then be D

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