A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 150 students who averaged 42 minutes concentrating on their professor during the hour lecture. The standard deviation was 12 minutes.
Round your answers to two decimal places.
A. The sampling distribution follows a ____ distribution.
B. With 95% confidence the population mean minutes of concentration is between_____ and_____ minutes.
C. If many groups of 150 randomly selected students are studied, then a different confidence interval would be produced from each group. About ______ percent of these confidence intervals will contain the true population mean number of minutes of concentration and about ______ percent will not contain the true population mean number of minutes of concentration.

Answers

Answer 1

Answer:

A. Normal

B. Between 40.08 minutes and 43.92 minutes.

C. About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

Question A:

By the Central Limit Theorem, a normal distribution.

Question B:

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{12}{\sqrt{150}} = 1.92[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.92 = 40.08 minutes

The upper end of the interval is the sample mean added to M. So it is 42 + 1.92 = 43.92 minutes

Between 40.08 minutes and 43.92 minutes.

Question C:

x% confidence interval -> x% will contain the true population mean, (100-x)% wont.

So, 95% confidence interval:

About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.


Related Questions

How do you factor x^3-2x^2+3x-6

Answers

Answer:

(x - 2) (x^2 + 3)

Step-by-step explanation:

x^3-2x^2+3x-6

Factor by grouping

Answer:

Factor by grouping

Step-by-step explanation:

[tex]x^{3}-2x^{2} +3x-6[/tex]

[tex]x^{2} (x-2) + 3 (x-2)[/tex]

[tex](x^{2} +3)(x-2)[/tex]

(5x2 + 4x + 3) - (2x2 - 2x + 5)

Answers

Answer:

3x^2+6x-2

Step-by-step explanation:

(5x2 + 4x + 3) - (2x2 - 2x + 5)

5x^2+4x+3-2x^2+2x-5

3x^2+6x-2

Solve the equation:
[3 2
5 5]

[x1
x2]+
[1
2]=
[2
-3]

Answers

9514 1404 393

Answer:

  (x1, x2) = (3, -4)

Step-by-step explanation:

As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.

  [tex]\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]+\left[\begin{array}{c}1\\2\end{array}\right]=\left[\begin{array}{c}2\\-3\end{array}\right]\\\\\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}1\\-5\end{array}\right]\\\\\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{5}\left[\begin{array}{cc}5&-2\\-5&3\end{array}\right]\left[\begin{array}{c}1\\-5\end{array}\right][/tex]

Performing the multiplication of the matrix by the vector gives the solution.

  x = ((5)(1) +(-2)(-5))/5 = 15/5 = 3

  y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4

Using your variables, x1, x2, the solution is ...

  (x1, x2) = (3, -4)


A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 ft, width 18 ft, and depth 4 ft. Suppose water is pumped out of the
pool at a rate of 216 ft per hour. If the pool starts completely full, how many hours does it take to empty the pool?
hours ( NO LINKS , LINK WILL GET YOU BANNED )

Answers

Answer:

10 hours (I am not positive)

Step-by-step explanation:

We first want to find the volume of pool which is 30 x 18 x 4 = 2160.

Then you are going to divide by 216 to find how many hours it takes to drain the whole pool. (I'm not that big of an expert)

The Y-Axis on a Coordinate plane runs vertical.

Answers

Answer:

good

Step-by-step explanation:

So when you do the (,) things the x-axis  would go first for example

say the x-axis=5 and the y-axis= 9 it would be (5,9)

hope this helps plz mark brainlest

What is the value of (5)3?​

Answers

Answer:

15

Step-by-step explanation:

This is simply just 5 x 3 = 15

BRAINLIST!!!
A construction crew built 7 1/2 miles of road in 3 1/8 days.
What is the unit rate in miles per day?

Write your answer as a fraction or a mixed number in simplest form.

Answers

Answer:

If you think numbers with fractions are annoying, consider transforming the number into fractions!

Step-by-step explanation:

7 1/2 is (14+1)/2, and 3 1/8 is (24+1)/3. Not you have 15/2 miles for 25/3 days and by dividing them you get 0.9 miles a day

Convert r=2/7sinθ−cosθ to rectangular form.

Enter your answer in slope-intercept form by filling in the blanks. Enter values so that fractions are simplified.

y=_/_x + _/_

Answers

Answer:

x²+y²=√(2/7 x-y)

is the answer, i think



Julie runs 3 miles each morning. How far does she run in feet?
(1 mile = 5,280 feet)

Answers

Answer:

15,840 feet

Step-by-step explanation:

5,280*3 = 15840

Since she runs 3 miles each morning, and 1 mile is 5,280,

then you multiply 5,280*3

Mr. Brown has 1/4pan of lasagna left in the refrigerator. He wants to cut the lasagna into equal slices so he can have it for dinner for 3 nights. What fraction of the whole lasagna will he eat each night?

Answers

Answer:

1/12

Step-by-step explanation:

He has a 1/4 pan left and wants to divide that into 3 equal pieces. So in night he will eat 1/3 of what he has left from the 1/4 pan. To figure out how much one slice is from an entire pan:

1/4 * 1/3  = 1/12

How many solutions are there in the following system of equations? (
one solution, no solutions, infinitely many solutions)
- 8x + 2y = -16
4x - y = 10 PLEASW HELP

Answers

Answer:

No solutions

Step-by-step explanation:

-8x+2y = -16

   4x-y  = 10 [multiply by 2 so it is easier to add/subtract]

-8x+2y = -16

8x -2y = 20

        0 = 4

0 and 4 cant be equal so theres no solution

Solve the Inequality Give 5 solutions of the inequality ( Show your solution).
2x -3 < 5

Answers

Answer:

Inequality Form:

x<4

1<4

3<4

-1004<4

Interval Notation:

(−∞,4)

(-1004,4)

(3,4)

(1,4)

Step-by-step explanation:

someone please help me answer this!!

Answers

Answer:

c = 85 in is the answer.

Step-by-step explanation:

a = 36 in

b = 77 in

c = ?

According to the Pythagoras theorem,

a² + b² = c²

36² + 77² = c²

1296 + 5929 = c²

7225 = c²

c = 85 in

∴ c = 85 in is the length of the missing leg.

You can use the pythagorean theorem which is a^2 + b^2=c^2
36^2+77^2=c^2
1296+5929=c^2
C^2=7225
C=-_/7225
C=85

The price of an item has been reduced by 45%. The original price was $63.
Use the ALEKS calculator to find the price of the item now.
se]
?

Answers

Answer:

$28.35

Step-by-step explanation:

[tex]45\% \times 63 \\ = 0.45 \times 63 \\ = 28.35[/tex]

Drag the word or expression to complete the function.

Answers

Answer:

-5 cos (2x)

Step-by-step explanation:

Reflection over x axis just means "multiply by -1" so the answer is

f(x) = 5 cos (2x)

g(x) = -5 cos (2x)

DUE IN THREE MINUTES
i give brainliest
factor each expression:
9+21
14+28
80+56

Answers

Answer:

Step-by-step explanation:

The secret trick to factoring is the greatest common factor.

The greatest common factor of 9 and 21 is 3. Thus, our expression is

3(3 + 7).

The greatest common factor of 14 and 28 is 7. Our expression is

7(2 + 4)

The greatest common factor of 80 and 56 is 8. This makes our expression

8(10 + 7).

Answer
3(3+7)
7(2+4)
8(10+7)

Suppose that in a random selection of 100 colored candies, 21% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%. Use the 0.01 significance level to test that claim.

Answers

Answer:

The pvalue of the test is 0.0784 > 0.01, which means that at this significance level, we do not reject the null hypothesis that the percentage of blue candies is equal to 29%.

Step-by-step explanation:

The candy company claims that the percentage of blue candies is equal to 29%.

This means that the null hypothesis is:

[tex]H_{0}: p = 0.29[/tex]

We want to test the hypothesis that this is true, so the alternate hypothesis is:

[tex]H_{a}: p \neq 0.29[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.29 is tested at the null hypothesis:

This means that [tex]\mu = 0.29, \sigma = \sqrt{0.29*0.71}[/tex]

Suppose that in a random selection of 100 colored candies, 21% of them are blue.

This means that [tex]n = 100, X = 0.21[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.21 - 0.29}{\frac{\sqrt{0.29*0.71}}{\sqrt{100}}}[/tex]

[tex]z = -1.76[/tex]

Pvalue of the test:

The pvalue of the test is the probability of the sample proportion differing at least 0.21 - 0.29 = 0.08 from the population proportion, which is 2 multiplied by the pvalue of Z = -1.76.

Looking at the z-table, z = -1.76 has a pvalue of 0.0392

2*0.0392 = 0.0784

The pvalue of the test is 0.0784 > 0.01, which means that at this significance level, we do not reject the null hypothesis that the percentage of blue candies is equal to 29%.

A bag contains 5 apples, 4 peaches, and 3 oranges. What is the probability of choosing an apple?

Answers

So it would be 5/12 which comes out to 0.41 so 41%

a gardener is growing tomato plants. one plant starts out 5 cm tall. it grows a constant 2 cm every week. what equation represents the height h of the plant after t weeks

a t= 5h+2
b t= 2h+5
c h=5t + 2
d h = 2t+5​

Answers

Answer:

D) h=2t+5

Step-by-step explanation:

1/3 divided by 7/6 can u solve it?????

Answers

Answer:

2/7

Step-by-step explanation:

when you divide a fraction by a fraction, flip the second fraction. 1/3 x 6/7 is 6/21, then you reduce it. divide 6 by 3 and 21 by 3, =2/7

Answer:

0.28571428571

Step-by-step explanation:

This is the calculated answer.

But after a lot of. technical,work the answer,ends up be 2/7

What is the smallest number of people you need for
the probability to be 100 percent that at least two of
them were born in the same month?

Answers

If I’m understanding the question right you’re asking the minimum amount of ppl in a group of some sort for the probability percentage to be 100, that at least 2 people were born same month.

I believe The answer would be two if this is the correct question

Solve the system of equations x - y = 12 and x + 7y = -20 by combining the
equations.

Answers

Answer:

x=16, y=-4

Step-by-step explanation:

-1(x-y=12)

x+7y=-20

-x+y=-12

x+7y=-20

8y=-32

y=-4

x-4=12

x=16

Answer:

x= 8, y= -4

Step-by-step explanation:

You can subtract one equation by another to eliminate x

(x-y)-(x+7y)=12-(-20)

-8y = 32

y= -4

Substitute y =  -4 in the first equation:

x-(-4) = 12

x =8

Name the ordered pair for point R

Answers

Can you post a picture please

Element X is a radioactive isotope such that every 26 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 390 grams, how long would it be until the mass of the sample reached 260 grams, to the nearest tenth of a year?​

Answers

Answer:

It will take 15.029 years for element X to reach mass of 260 grams

Step-by-step explanation:

The half life period of radioactive element X is 26 years

The initial mass of radioactive element X is 260 grams

Elapsed time = half life * log (beginning amount /ending amount)/log 2

Substituting the given values, we get

Elapsed time = 26 * log (390/260)/log 2

=  15.209 years

What is the volume of a sphere with a diameter of 22ft? Round your answer to the nearest cubic foot.
8359 cubic feet
6193 cubic feet
• 2786 cubic feet
5572 cubic feet

Answers

Answer:

D) 5,572

Step-by-step explanation:

4/3×pi×r^3

4/3×3.14×11^3

5572.453...

5572

can i please have some actual help with this?

Answers

Answer:

x = 286.01 inches

Step-by-step explanation:

Given that,

Height of the ramp, H = 20 inches

Angle of elevation, [tex]\theta=4^{\circ}[/tex]

We need to find the value of x. It can be solved using trigonometry as follow :

[tex]\tan\theta=\dfrac{P}{B}[/tex]

Where

P is perpendicular and B is base

So,

[tex]\tan(4)=\dfrac{20}{x}\\\\x=\dfrac{20}{\tan(4)}\\\\x=286.01\ in[/tex]

So, the value of x is equal to 286.01 inches.

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.

I need help but the green is correct but I need help with the first 2 I need to turn this in 10 mins

Answers

Answer: see work

Step-by-step explanation:

Blue:

9-5+3x4

Red:

10+6/3+8x2

Answer:

Work

Step-by-step explanation:

Blue:

9-5+6-5

Red:

4+4+5

A survey of 71 families showed that:
40 have a son(s)
45 have a daughter(s)
18 had neither a son nor a daughter.
How many families had ONLY son(s)?​

Answers

Answer:

108

Step-by-step explanation:

10. What is the perimeter of the figure on the coordinate plane below?

A 32 units
B 24 units
C 22 units
D 14 units

Answers

Answer:

24 units

Step-by-step explanation:

Each line plot equals 2, so the length is 8 and the hight is 4. 8+8+4+4 = 16 + 8 = 24 units.

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