In a study of academic procrastination, the authors of a paper reported that for a sample of 451 undergraduate students at a midsize public university preparing for a final exam in an introductory psychology course, the mean time spent studying for the exam was 7.74 hours and the standard deviation of study times was 3.10 hours. For purposes of this exercise, assume that it is reasonable to regard this sample as representative of students taking introductory psychology at this university.
(a) Construct a 95% confidence interval to estimate μ, the mean time spent studying for the final exam for students taking introductory psychology at this university. (Round your answers to three decimal places.) TWO VALUES
(b) The paper also gave the following sample statistics for the percentage of study time that occurred in the 24 hours prior to the exam.
n = 451 x = 43.78 s = 21.96
Construct a 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam. (Round your answers to three decimal places.)

Answers

Answer 1

Answer:

a) The 95% confidence interval to estimate μ is (7.435, 8.045) hours.

b) The 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam is (41.079%, 45.481%).

Step-by-step explanation:

Question a:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{3.3}{\sqrt{451}} = 0.305[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 7.74 - 0.305 = 7.435 hours

The upper end of the interval is the sample mean added to M. So it is 7.74 + 0.305 = 8.045 hours.

The 95% confidence interval to estimate μ is (7.435, 8.045) hours.

Question b:

90% confidence interval means that [tex]Z = 1.645[/tex]

The margin of error is:

[tex]M = 1.645\frac{21.96}{\sqrt{451}} = 1.701[/tex]

43.78 - 1.701 = 41.079%

43.78 + 1.701 = 45.481%

The 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam is (41.079%, 45.481%).


Related Questions

what is the value of 4/15÷2/3​

Answers

Answer:

2 /5

Step-by-step explanation:

5m²+15m=0

t²-5t+6=0

5p²+12p+4=0

2a²+10a-48=0

x(2x+5)=0

Answers

Answer:

m=1, m= -3

t=3, t=2

p= -0.4, p= -2

a= 3, a= -8

x=0, x= -2.5

Answer:

I hope this helps a little bit.

It Is Not Fake

It Got Answers Promise

Help me please, I don’t understand this at all

Answers

Answer: d

Step-by-step explanation:

aint no 90 cuz

Answer:

Not a right triangle

Step-by-step explanation:

root 4^2 + 6^2 is not equal to 7.5

n a study to investigate whether vitamin C will prevent colds, 400 subjects are assigned at random to one of two groups. The experimental group takes a vitamin C tablet daily, while the control group takes a placebo. At the end of the experiment, the researchers calculate the difference between the percentage of subjects in the two groups who were free of colds. This difference is statistically significant (P=0.03) in favor of the vitamin C group.

Answers

Answer:

Step-by-step explanation:

The aim of this question is to see if we can infer and conclude that vitamin C has a good impact in preventing colds based on the evidence provided.

Null hypothesis: Vitamin C has no effect on preventing colds.

Alternative hypothesis: Vitamin C has a strong effect on preventing colds.

Assuming, significance level = 0.05

Since the p-value for the difference is 0.03 which is less than 0.05.

Hence, the null hypothesis is rejected (which is there is no effect of vitamin C).

As a result, it can be concluded that Vitamin C has a major impact on the prevention of colds.

the price per gallon of gas with a $7 car wash is $3.19 and the price without the car wash is $3.39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?

Answers

Answer:

The price per gallon of gas with a $7 car wash is $3.19

Then if you purchase x gallons of gas and also pay for the car wash, the total cost is:

C(x) = $7 + $3.19*x

In the case that you do not pay for the car wash, the cost per gallon is $3.39

Then the cost for x gallons of gas in this case is:

K(x) = $3.39*x

When is it worth it to buy the car wash?

We need to sett the equations:

C(x) = K(x)

This means that you pay exactly the same in both cases, but in one ( C(x)) you get the car wash and in the other not.

Then we need to solve:

$7 + $3.19*x = $3.39*x

$7 = ($3.39 - $3.19)*x = $0.20*x

$7/$0.20 = x = 35

Then for 35 gallons, is worth to buy the car wash.

In the case where the car wash costs $2, then the equation C(x) becomes:

C(x) = $2 + $3.19*x

Then if we solve the same equation:

C(x)  =K(x)

$2 + $3.19*x = $3.39*x

$2 = ($3.39 - $3.19)*x

$2 = $0.20*x

$2/$0.20 = x

10 = x

Then for 10 galons is whort  buy the car wash.

Find the value of f(4) for the function

Answers

Answer:

f(4) = 7

Step-by-step explanation:

The notation for these type of problems is very confusing. Just remember that f(x) is the same thing as y (or some variable). Even if there is a number or something on the inside of the parentheses, it's still just a variable.

In our case

f(a) = 2(a + 4) -9

could be rewritten as

y = 2(a + 4) - 9

the thing on the inside of the parentheses signifies what the equation is dependent on.

so when is says f(4), it just want's you to trade out a for a 4, but the equation is still the same.

f(4) = 2((4) + 4) - 9

Now, just follow the order of operations

f(4) = 2(8) - 9

f(4) = 16 - 9

f(4) = 7

I need help with a Delta math Assignment

Gabriella made 5% of her free throws over the season. If she shot 180 free throws, how many did she make?

Answers

Answer:

9

Step-by-step explanation:

The volume of a fish tank is 70 cubic feet. If the density is 0.4 fish over feet cubed, how many fish are in the tank?

175
88
28
14

Answers

Answer:

28 fish is the correct answer

Step-by-step explanation:.

The number of fish in the fish tank will be 28.

What is a volume?

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the Cuboid.

The density of the fish is defined as the number of fish per unit volume of the tank.

Given that volume of a fish tank is 70 cubic feet and the density is 0.4 fish over feet cubed.

The number of fish is calculated as below:-

Number = Volume of tank x Density of fish

Number = 70 x 0.4

Number = 28 fish

Therefore, the number of fish in the fish tank will be 28.

To know more about volume follow

https://brainly.com/question/1972490

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Which statement can be used to find X

Answers

Answer:

it's letter D. cos 16⁰=²¹--x

Please only answer if you're 100% sure it's correct. Thank you. (It's pretty easy.)

Answers

2x-7 and 2+7 are the answers

simplify 8x+7-x-4


help meeeeee!!!​

Answers

Answer:

7x + 3

Step-by-step explanation:

Let's simplify step-by-step.

8x + 7 − x − 4

= 8x + 7 + −x + −4

Combine Like Terms:

= 8x + 7 + −x + −4

= (8x + −x) + (7 + −4)

= 7x + 3

Answer:

= 7x + 3

hope this helps and is right. p.s i really need brainliest :)

if my answer is wrong then I am incredibly sorry!

Sin 17° cos 13° + cos 17° sin 13°​

Answers

Answer:

.5

Step-by-step explanation:

Sin(x)cos(y) + cos(x)sin(y) = sin(x+y)

sin(17+13) = 1/2

what is the answer to this?

Answers

Answer:

i can only say that you should use this forumla, the sins law

sin(a)/A = sin(b)/B = sin(c)/C

Step-by-step explanation:

What is the approximate value of 12−−√ ?


3.5


2


6


4.5

Answers

The answer is 3.5. Do you need me to explain or is that ok?

someone please help me answer this!!

Answers

Answer:

c = 8.4m is the answer.

Step-by-step explanation:

a = 6m

b = 6m

c = ?

According to the Pythagorean theorem,

a² + b² = c²

6² + 6² = c²

36 + 36 = c²

c² = 72

c = 8.4m

∴ The mouse runs 8.4 m from the opposite corners of the room.

Answer:

8.5 m

Step-by-step explanation:

If you draw the segment from one corner to the opposite corner, you'll have the hypotenuse of a triangle with two legs of 6 m. We can find the length of the hypotenuse using the Pythagorean Theorem.

a^2 + b^2 = c^2

6^2 + 6^2 = c^2

36 + 36 = c^2

c^2 = 72

c = sqrt(72)

c = 6sqrt(2) = 8.5

Answer: 8.5 m

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