According to a report an average person watched 4.55 hours of television per day in 2005. A random sample of 20 people gave the following number of hours of television watched per day for last year. At the 10% significance level, do the data provide sufficient evidence to conclude that the amount of television watched per day last year by the average person differed from that in 2005? 1.0 4.6 5.4 3.7 5.2 1.7 6.1 1.9 7.6 9.1 6.9 5.5 9.0 3.9 2.5 2.4 4.7 4.1 3.7 6.2 a. identify the claim and state and b. find the critical value(s) and identify the rejection region(s), c. find the standardized test statistic Sketch a graph decide whether to reject or fail to reject the null hypothesis, and d. interpret the decision in the context of the original claim. e. Obtain a 95%confidence interval

Answers

Answer 1

Answer:

a. The claim is that the amount of television watched per day last year by the average person differed from that in 2005.

b. The critical values are tc=-1.729 and tc=1.729.

The acceptance region is defined by -1.792<t<1.729. See the picture attached.

c. Test statistic t=0.18.

The null hypothesis failed to be rejected.

d. At a significance level of 10%, there is not enough evidence to support the claim that the amount of television watched per day last year by the average person differed from that in 2005.

e. The 95% confidence interval for the mean is (2.29, 7.23).

Step-by-step explanation:

We have a sample of size n=20, which has mean of 4.76 and standard deviation of 5.28.

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{20}(1+4.6+5.4+. . .+6.2)\\\\\\M=\dfrac{95.2}{20}\\\\\\M=4.76\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{19}((1-4.76)^2+(4.6-4.76)^2+(5.4-4.76)^2+. . . +(6.2-4.76)^2)\\\\\\s=\dfrac{100.29}{19}\\\\\\s=5.28\\\\\\$

a. This is a hypothesis test for the population mean.

The claim is that the amount of television watched per day last year by the average person differed from that in 2005.

Then, the null and alternative hypothesis are:

$H_0: \mu=4.55\\\\H_a:\mu\neq 4.55$

The significance level is 0.1.

The sample has a size n=20.

The sample mean is M=4.76.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=5.28.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.28}{\sqrt{20}}=1.181$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.76-4.55}{1.181}=\dfrac{0.21}{1.181}=0.18$

The degrees of freedom for this sample size are:

$df=n-1=20-1=19$

The critical value for a level of significance is α=0.10, a two tailed test and 19 degrees of freedom is tc=1.729.

The decision rule is that if the test statistic is above tc=1.729 or below tc=-1.729, the null hypothesis is rejected.

As the test statistic t=0.18 is within the critical values and lies in the acceptance region, the null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of television watched per day last year by the average person differed from that in 2005.

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=4.76.

The sample size is N=20.

The standard error is s_M=1.181

The degrees of freedom for this sample size are df=19.

The t-value for a 95% confidence interval and 19 degrees of freedom is t=2.093.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.093 \cdot 1.181=2.47$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 4.76-2.47=2.29\\\\UL=M+t \cdot s_M = 4.76+2.47=7.23$

The 95% confidence interval for the mean is (2.29, 7.23).

Related Questions

Find all zeros real and nonreal

Answers

The zeros of the function are:

real zeros: -1 and 3nonreal zeros: ±3i

How to determine the zeros of the function

The equation of the function is given as

f(x) = x⁴ - 2x³ + 6x² - 18x - 27

When the function is factored, we have the following equation

f(x) = (x + 1)(x - 3)(x² + 9)

Next, we set the function to 0

So, we have the following

(x + 1)(x - 3)(x² + 9) = 0

The above means that

(x + 1) = 0 or (x - 3) = 0 or (x² + 9) = 0

When evaluated. we have

x = -1 or x = 3 or x² = -9

So, we have

x = -1 or x = 3 or x = ±3i

The above are the zeros of the equation

Read more about polynomial functions at

https://brainly.com/question/7693326

#SPJ1

Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG. The measure of angle HGF is (9y + 3)°, and the measure of angle EFG is (8y + 5)°. What is the measure of angle HGF?

Answers

Answer:

21°

Step-by-step explanation:

In an sosceles trapezoid, the lower base and upper base angles are congurent

⇒ ∠HGF = ∠EFG

⇒ 9y + 3 = 8y + 5

⇒ 9y - 8y = 5 - 3

⇒ y = 2

⇒ ∠HGF = 9(2) + 3

= 18 + 3

= 21

Final answer:

The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.

Explanation:

This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.

Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.

Learn more about Isosceles Trapezoid Angle Measure here:

https://brainly.com/question/32850813

#SPJ11

consider a production process that produces batteries. a quality engineer has taken 20 samples each containing 100 batteries. the total number of defective batteries observed over the 20 samples is 200. the sample standard deviation is

Answers

The sample standard deviation is 0.03

As per the given data, a quality engineer has taken the 20 samples in which each containing of 100 batteries.

The total number of the defective batteries which are observed over the 20 samples is 200.

Here we have to calculate the value of the sample standard deviation

The number of samples, k = 20

The number of batteries in each sample:

The sample size = 100

The total number of batteries of the sample are:

The total number of samples, $$\sum{n=20 \times 100=2000}$$

$& \bar{n}=\sum_\frac{n}{k}} \\$

= $$\frac{2000}{20}$

= 100

The total number of defective batteries = 200

Now we can calculate the proportion of the deflective battery:

Therefore, $$\bar{p}=$$ The total number of defectives ÷ The total number of samples

= $$\frac{200}{2000}$

= 0.10

The standard deviation, $$\sigma_{\mathrm{p}}=\sqrt{\frac{\bar{p} \bar{q}}{\bar{n}}}$$

= $$ \sqrt{\frac{0.1 \times 0.9}{100}} \\$

= $& \sqrt{0.0009} \\$

= 0.03

For more questions on sample standard deviation

https://brainly.com/question/1418491

#SPJ4

your are planning a birthday Party at Chuck E Cheese for your little brother? your total budget for the party is $500
There is a fee of $302 to hold your party there and a $15 fee for each guest

How many guests,g ,can you invite to your little brother birthday party?
(The answer come greater than or equal to)

Answers

Answer:

Step-by-step explanation:

500 - 302=198

198 divided by 15 = 13. 2 round down to 13. 13 guests.

in a set of 5 numbers the average of two is 12 the average of the other 3 is 7 what is the average of all five numbers. (fraction or whole number)

Answers

Answer:

The average of all 5 numbers is 9

Step-by-step explanation:

Two of the numbers average 12. That means that their total is 2*12 = 24

Three of the other numbers average 7. That means that their total is 7*3 = 21

The total score for the 5 numbers is 24 + 21 = 45

The average for all 5 numbers is 45/5 = 9

I’m stuck, help would be nice :D

Answers

Answer:

-14

Explanation:

3 x -3 - 5 = -14

Answer:

-14, -5, 4, and 13

Step-by-step explanation:

For each x value, substitute it for x in the equation.

For the first one where x = -3,

y = 3(-3) - 5

y = -9 - 5

y = -14

So the first one is -14. The next x value is 0

y = 3(0) - 5

y = 0 - 5

y = -5

Second one is -5. The next x value is 3

y = 3(3) - 5

y = 9 - 5

y = 4

Third is 4. The next x value is 6

y = 3(6) - 5

y = 18 - 5

y = 13

So the last one is 13.

pt 2 7-7 Please helppp If you guys want lol ill do 7 moreeee LOL

Answers

Answer:

c = 72

Step-by-step explanation:

x ___c__ = 9 x 8

c = 72

Hi there! Hopefully this helps!

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

Answer: c = 72~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\frac{c}{8} = 9$

Multiply both sides by 8.

$c = 9 \times 8$

Multiply 9 and 8 to get, you guessed it, 72!

Equation of the line passing through (7,5) and (1, 2)

Answers

Answer:

$y = \frac{1}{2}x + \frac{3}{2}$

Step-by-step explanation:

Assuming this is a linear equation in the form of $y = mx + b$, we can first solve for the slope using $\frac{y_2 - y_1}{x_2 - x_1}$, for these points, the slope would be $\frac{1}{2}$. Now we plug in the points to get the equation:

plugging in (7,5), we get $5 = \frac{1}{2}$ ×$7$ + $b$

and solving for b, we get b = $\frac{3}{2}$

therefore, the equation of the line passing through (7,5) and (1,2) is $y = \frac{1}{2}x + \frac{3}{2}$.

hope this helps!

solve for y please help me image is attached and will give 5 stars :)

Answers

Answer:

Step-by-step explanation:

If you match up the pieces then you would find that the missing side/green blank is 8

Which equation represents the total number of black and white squares on the chess board?

Answers

The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

How to determine the equation of the black and white squares

From the question, we have the following parameters that can be used in our computation:

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

Answers

Answer:c

Step-by-step explanation:

Answer:b

Step-by-step explanation:

A high school robotics club sold cupcakes at a fundraising event.

They charged $2.00 for a single cupcake, and $4.00 for a package of 3 cupcakes.
They sold a total of 350 cupcakes, and the total sales amount was $625.
The system of equations below can be solved for , the number of single cupcakes sold, and , the number of packages of 3 cupcakes sold.

Multiply the first equation by 2. Then subtract the second equation. What is the resulting equation?

x + 3y = 350
2x + 4= 625

Type your response in the box below.

$$

Answers

The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:

-5y = -375

1. Given equations:

- x + 3y = 350 (Equation 1)

- 2x + 4y = 625 (Equation 2)

2. Multiply Equation 1 by 2:

- 2(x + 3y) = 2(350)

- 2x + 6y = 700 (Equation 3)

3. Subtract Equation 2 from Equation 3:

- (2x + 6y) - (2x + 4y) = 700 - 625

- 2x - 2x + 6y - 4y = 75

- 2y = 75

4. Simplify Equation 4:

-2y = 75

5. To isolate the variable y, divide both sides of Equation 5 by -2:

y = 75 / -2

y = -37.5

6. Therefore, the resulting equation is:

-5y = -375

For more such questions on multiplying, click on:

https://brainly.com/question/29793687

#SPJ8

QUESTION 7
If license plates in Idaho have 4 numbers followed by 2 letters, how many different plates can be made?
a. 6,760,000
O b. 676
O c. 260
O d. 17,576,000

Answers

the answer is d. 17,576,000

The number of different license plates that can be made in Idaho with 4 numbers followed by 2 letters is 6,760,000, option a is correct.

To determine the number of different license plates that can be made in Idaho with 4 numbers followed by 2 letters, we need to consider the possibilities for each element.

For the numbers, we have 10 options (0-9) for each of the four positions, resulting in a total of $10^4 = 10,000$ combinations.

For the letters, we have 26 options (A-Z) for each of the two positions, resulting in a total of $26^2 = 676$ combinations.

To find the total number of different plates, we multiply the number of possibilities for each element:

$10,000 \times 676 = 6,760,000$.

Hence, option a is correct.

To learn more on Combinations click:

https://brainly.com/question/19692242

#SPJ4

Select the equivalent expression (x^ -3 * y^ 3 )^ -7 =?

Answers

Answer:

Step-by-step explanation:

Write the expression as a single power of b.

open parentheses b to the power of begin display style 3 over 4 end style end exponent over b to the power of begin display style 1 fourth end style end exponent close parentheses to the power of 1 half end exponent

Answers

The simplified form of the given expression is x raise to the power of one-thirty.

What is an expression?

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Simplifying indices expressions

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

Learn more on indices here:

brainly.com/question/10339517

#SPJ1

A metal piece has four ridges of equal size on the top. The width of the piece is 3cm. Find the volume. Show your work

Please help soon I give 30 brainly

Answers

In a case whereby the metal piece has four ridges of equal size on the top. The width of the piece is 3cm the volume of the work is $450cm^3$

How can the volume be found?

Based on the provided fiqure, we will need to find te volume of the rectangle, then substract from th volume of the four triangular prism

The volume of the rectangle can be epresed as ;

2*3*10 = $600cm^3$

The volume of the four triangular prism can be expressed as

20/4 = 5cm 10-5= 5cm

$1/2 * 5 * 5*3*4 = 150cm^3$

$600- 150 =450 cm^3$

Learn more about volume at:

https://brainly.com/question/27710307

#SPJ1

4.
What would be the purchase price for a $5,000, 91-day T-bill paying 3%
interest?
a. $4,925.00
b. $4,962.50
C. $5,000.00
d. $5,037.50

Answers

Answer:

Step-by-step explanation:

A = P(1+i/n)^t

5000 = P(1+0.03/(361.3/91)^1 361.3 ??? it worked

P = 5000/1.007556048

P = $4962.50309

the 91 day T-bill confused by financial calculator which got $4962.78 for a quarterly compound interest rate

Can you please please help me with this please it’s so hard and i will give you a branlist

Answers

i think it’s the parallel sides “b”

Whoever answers gets brainlist!

Answers

Answer: The Correct Answer is 6 because 16+24 is 40 then minus 10 is 30

16-15 is 1 then plus 4 is 5 then you divide 30 by 5 and get 6

Step-by-step explanation: BRAINLIEST PLS

Answer:

I'm pretty sure its 6.

Step-by-step explanation:

find the difference of (-10x^2 + 5x -3) and (4x^2 + 6x - 7)

Answers

Answer:

-14x² - x + 4

Step-by-step explanation:

(-10x² + 5x - 3) - (4x² + 6x - 7)

= (-10x² + 5x - 3) - (+4x²) - (+6x) - (-7)

= (-10x² + 5x - 3) -4x² -6x +7

= -10x²-4x² +5x-6x -3+7

= -14x² - x + 4

Two bags of carrots cost a total of $4.00. If each bag weighs half a pound, what is the cost, in dollars, per ounce of carrots?

Answers

Answer:

1.50

Step-by-step explanation:

Video games sold: x
Revenue function: R(x) = 60X
Cost function: C(x) = 12 + 7x
Profit function: P(x) =
DONE
What is the profit earned from selling 20 video games

Answers

The answer to this problem is 1048$

what should be subtracted from 7/12+7/8 to obtain the multiplicated inverse of (4/3-4/9)

Answers

To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

A sequence of transformations map ABC to A’B’C. The sequence of transformations that maps ABC to A’B’C is a reflection across the _ followed by a translation _

Answers

The sequence of transformations that maps ABC to A’B’C is a reflection across the line y = x followed by a translation of 10 units right and 4 units up.

How to obtain the transformations?

The equivalent vertices C and C' are given as follows:

C(-4, 2).C'(12,0).

Considering the change in the orientation of the figure, it was reflected over the line y = x, for which the rule is given as follows:

(x,y) -> (y,x).

Hence:

(-4,2) -> (2,-4)

To go from (2,-4) to (12,0), the translation rule is given as follows:

(x,y) -> (x + 10, y + 4)

Hence the translation is defined as follows:

10 units right and 4 units up.

More can be learned about transformations in a figure at https://brainly.com/question/28687396

#SPJ1

What is the difference in rainfall from the wettest and driest months ?

Answers

The difference in rainfall between the wettest and driest months is the amount of precipitation.

What do you mean by precipitation?

Precipitation refers to any form of moisture that falls from the atmosphere to the ground, including rain, snow, sleet, hail, and other forms of precipitation. Precipitation is an important aspect of the Earth's water cycle, as it provides the water that replenishes rivers, lakes, and aquifers, and sustains the growth of plants and animals.

The amount of precipitation that falls in a given area can vary widely, depending on many factors such as geography, temperature, and prevailing weather patterns. For example, areas near the equator tend to receive more rainfall than areas located closer to the poles, and areas with high elevations tend to receive more snow than areas that are closer to sea level.

The distribution of rainfall and other forms of precipitation across a region can also be affected by the prevailing winds, air masses, and topographical features. For example, mountainous areas may receive more rainfall due to the prevailing winds and the way that air masses interact with the terrain.

The difference in rainfall between the wettest and driest months is the amount of precipitation that occurs in the wettest month minus the amount of precipitation that occurs in the driest month. This difference can vary greatly depending on the location and climate of a region.

To know more about climate visit:

https://brainly.com/question/28388440

#SPJ1

in the illustration below ,The two lights are designed tc pperate at 6 volts, 5 amps each,
5
f the power source is12 volts, what will be the value of the Resistor?
Round to the tenth position. (0.00)

Answers

The value of the resistor needed in this scenario is approximately 1.2 ohms.

To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.

Using Ohm's Law, we have the formula:

V = I * R

Where:

V is the voltage across the resistor (12 volts in this case),

I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),

R is the resistance of the resistor (which we need to find).

Rearranging the formula, we have:

R = V / I

Plugging in the values:

R = 12 volts / 10 amps

R = 1.2 ohms

Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.

It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.

For more such question on resistor visit:

https://brainly.com/question/4703820

#SPJ8

Braden multiples a whole number by a unit fraction.The whole number is greater than the denominator of the fraction. Will the product be greater than 1? Explain.

Answers

The product of a whole number multiplied by a unit fraction will be less than the whole number

what is unit fraction?

A unit fraction is a fraction where the numerator is always 1 and the denominator is a positive integer. In other words, it represents a single part (unit) of a whole that has been divided into equal parts. For example, 1/2, 1/3, 1/4, and 1/5 are all unit fractions. Unit fractions are sometimes used in mathematics and in other fields such as economics, where they can be used to represent percentages or proportions of a whole.

It depends on the specific value of the unit fraction and the whole number.

A unit fraction is a fraction where the numerator is 1, and the denominator is a positive integer. So, the fraction is less than or equal to 1. Multiplying a whole number by a unit fraction will result in a product that is less than or equal to the whole number.

If the whole number is greater than the denominator of the unit fraction, then the fraction is less than 1. Multiplying a number that is greater than the denominator by a fraction that is less than 1 will result in a product that is less than the original whole number.

Therefore, in general, the product of a whole number multiplied by a unit fraction will be less than the whole number, and it will be less than 1 if the fraction is less than 1. However, there may be some specific cases where the product is greater than 1, but they would be exceptions rather than the rule.

To learn more about unit fraction from the given link

https://brainly.com/question/30947533

#SPJ1

Please help will mark Brainly

Answers

A.
The number of tickets day and evening combined should be more then 8 since it says at least 8 tickets. However the cost of the tickets which is 15x+30y (multiply the amount of tickets bought by the cost) should be less then 300 bucks since they have a budget. Hope this helps!

Someone help
in the 2006 World cup, circles of cloth were used to cover the centre circle at the start of each match . The radius of a centre circle is 9.15m and 12 football pitches were used . Estimate the total area of cloth used .

Answers

The total area of clothes used is 12627m².

How to calculate the area?

It is important to note that a football is in the shape of a sphere. Therefore, the area of a ball will be:

= 4πr²

In this case, the radius which is represented by r is given as 9.15m.

The area will be:

= 4πr²

= 4 × 3.142 × 9.15²

= 1052.22

Therefore, since there are 12 pitches, the area will be:

= 1052.22m² × 12

= 12627m²

Learn more about area on:

brainly.com/question/25292087

#SPJ1

Please help!!! Make up a word problem that the following equation could
represent:
5x + 9 = 44

Answers

Answer:

Marissa buys 5 bottles of soda which cost X, she also buys a 9 dollar meal. If her total cost was 44 dollars, how much does each bottle cost?

Step-by-step explanation:

Answer:

there was was 5 fish in the tank and a shipment of x amount plus nine recent babies were born? equaling to 44 in total?

Step-by-step explanation:

Other Questions