Researchers are studying rates of homeowners in a certain town. They believe that the proportion of people ages 36-50 who own homes is signifificantly greater than the proportin of people age 21-35 who own homes and want to test this claim. The results of the surverys are: Homeowners Renters Total


Ages 21-35 18 38 56



Ages36-50 40 22 62


TOTAL 58 60 118



What are the null hypothesis and alternative hypothesis for this situation

Answer:

0.95%

Step-by-step explanation:

Simply divide 100 with 460 then multiply 4.37

100/460 = 0.2173913043

Multiply by 4.37 and you get 0.95

Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent​ switches, each one set on or off. The receiver​ (wired to the​ door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches​ independently.The probability of at least one pair of neighbors using the same​ settings is 0.65633

Step-by-step explanation:

Step 1

In the question it is given that

Automatic garage door opener utilizes a transmitter control with four independent​ switches

So .the number of Combinations possible with the Transmitters =

2*2*2*2= 16

Step 2

Probability of at least one pair of neighbors using the same settings = 1- Probability of All Neighbors using different settings.

= 1- 16*15*14*13*12*11/(16^6)

Step 3

Probability of at least one pair of neighbors using the same settings=

= 1- 0.343666

Step 4

So the probability of at least one pair of neighbors using the same settings

is  0.65633

Answer:

4 action figures per friend

Step-by-step explanation:

To split the 12 action figures between 3 friends, divide 12 by 3.

12/3 = 4

Therefore, each friend gets 4 action figures.

Answer:

each friend gets 12 divided by 3 action figures. Each friend gets 12/3 action figures. Each friend gets 4 of the 12 action figures.

Step-by-step explanation:

i put this and i got it right.

Answer:

Depending upon the golf score predictors we can conclude the answer from given Conditional statements

If Someone want Total golf score better then, following .condition

Yes, Because R squared is close to 1 .  ....(If Regression values are prefect to fit with model then only)

(But the data is not sufficient to say 100%, it depends on score given)

Step-by-step explanation:

Given :

Explanatory Question on r-squared in regression.

To Find :

Does regression equation help us to know total golf score much better.

Solution;

As  in Question there is no golf score given so we cant see "yes" or "no".

But we can be conditional here ,

1) If golf score to be accurate then , multiple regression predict points should fit the model prefect ,hence the R squared value "must be close to 1" .

2) If gold score is not accurate then multiple regression   suggest that model does  not explain any variables, no linear relationship.

then r squared value "must not be close to 1".

Depending upon the golf score predictors we can conclude the answer from given Conditional statements.

that  Yes, Because R squared is close to 1 .

Answer:

x^2-7x+6

Step-by-step explanation:

(x-6)(x-1)

x^2-1x-6x+6

x^2-7x+6

The quadratic function whose zeros are 6 and 1 is: f(x) = x² - 7x + 6.

To write a quadratic function f(x) with zeros at x=6 and x=1, we can start by representing it in factored form:

f(x) = a(x−6)(x−1)

Where a is a constant. Depending on the desired leading coefficient, you can choose any value for a. For simplicity, let's choose a=1.

Therefore, the quadratic function with zeros at 6 and 1 is:

f(x) = (x−6)(x−1)

f(x) = x² − 7x + 6

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Answer:

54.1607142857

Step-by-step explanation:

just simplify it

The approximate value of -3,033 divided by -56 is -54 when rounded to two significant figures.

To approximate the value of -3,033 ÷ (-56), you can perform the division by changing both numbers into their absolute values and divide normally as the negative signs will cancel each other out. This results in the division of 3,033 by 56. Using a calculator, you would get 54.1607142857. However, since we need an approximate value with two significant figures, the result would be rounded to -54.

Answer:

t = 2.9517 min

Step-by-step explanation:

Given

D = 40 m ⇒ R = D/2 = 40 m/2 = 20 m

ybottom = 2 m

ytop =  ybottom + D = 40 m + 2 m = 42 m

yref = 34 m

t = 10 min

The height above the ground (y) is a sinusoidal function.

The minimum height is ybottom = 2 m

The maximum height is ytop = 42 m;

The midline is (ybottom + ytop)/2 = (2 m + 42 m)/2 = 22 m

If we model the wheel as follows

x² + y² = R²

where

y = yref - (R + ybottom) = 34 m - (20 m + 2 m) = 12 m

R = 20 m

we have

x² + (12 m)² = (20)²

⇒ x = 16 m

then

tan (θ/2) = x/y

⇒ tan (θ/2) = 16 m/12 m

⇒ θ = 106.26°

Knowing the angle of the circular sector, we apply the relation

t = (106.26°)*(10 min/360°)

⇒ t = 2.9517 min

Since the period of revolution is 10 minutes, the ride is above 34 meters for 2.9517 minutes each revolution.

To determine how many minutes of the ride are spent higher than 34 meters, trigonometry can be used to find the proportion of the ride above this height. This results in a total time of 3.136 minutes spent higher than 34 meters.

This problem involves trigonometric calculations to solve real-world scenarios. A Ferris wheel is a circle, and when you boarded at the six o'clock position you are 2 meters above the ground. The diameter of this Ferris wheel is 40 meters, so the radius is 20 meters. The highest point you can get to on the Ferris wheel is the diameter plus the height of the platform, or 42 meters. We want to know how much time is spent higher than 34 meters.

When you are 34 meters in the air, you are 16 meters above the centre of the wheel (because the center is 20 + 2 = 22 meters off the ground). The angle θ that satisfies this condition is the arcsin of 16/20, which is 56.44 degrees (or 0.986 radians). Since the Ferris wheel turns around completely, we should consider the same angle on the other side of the wheel, meaning you spend 2*56.44 = 112.88 degrees or (112.88/360) = 31.36% of the time above 34 meters. Since one full revolution takes 10 minutes, this corresponds to 31.36% * 10 = 3.136 minutes above 34 meters.

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Answer:

how do you thik,,, n vm

Step-by-step explanation:

Answer:

[tex]\lambda=8,\ \lambda=-5[/tex]

Step-by-step explanation:

Eigenvalues of a Matrix

Given a matrix A, the eigenvalues of A, called [tex]\lambda[/tex] are scalars who comply with the relation:

[tex]det(A-\lambda I)=0[/tex]

Where I is the identity matrix

[tex]I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

The matrix is given as

[tex]A=\left[\begin{array}{cc}3&5\\8&0\end{array}\right][/tex]

Set up the equation to solve

[tex]det\left(\left[\begin{array}{cc}3&5\\8&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda \end{array}\right]\right)=0[/tex]

Expanding the determinant

[tex]det\left(\left[\begin{array}{cc}3-\lambda&5\\8&-\lambda\end{array}\right]\right)=0[/tex]

[tex](3-\lambda)(-\lambda)-40=0[/tex]

Operating Rearranging

[tex]\lambda^2-3\lambda-40=0[/tex]

Factoring

[tex](\lambda-8)(\lambda+5)=0[/tex]

Solving, we have the eigenvalues

[tex]\boxed{\lambda=8,\ \lambda=-5}[/tex]

Answer:

Step-by-step explanation:

Hi there,

The graph indicated is showing a horizontal asymptote. In fact, it is showing both a horizontal and a vertical asymptote.

To tell which type it is, notice where the graph "shoots off" and almost forms an imaginary straight line in one direction. Using this logic, the horizontal asymptote will be exactly horizontal, parallel to x-axis, and vertical asymptote will be exactly vertical, parallel to y-axis.

With this graph, we notice the horizontal asymptote is at y=0, where the x-axis is. The vertical asymptote is bit more difficult to determine graphically, but can definitely say it is past x=-10. We could determine it if we had the function, but that is not necessary for this question.

Study well, and persevere. If you liked this solution, leave a Thanks or give a rating!

thanks,

Final answer:

A horizontal asymptote is a horizontal line that a curve approaches but never touches as the x-values (or y-values) go to positive or negative infinity. In the case of the function y = 1/x, the graph has a horizontal asymptote at y = 0.

Explanation:

A horizontal asymptote is a horizontal line that a curve approaches but never touches as the x-values (or y-values) go to positive or negative infinity. To determine if a function has a horizontal asymptote, we need to analyze the behavior of the function as x approaches positive or negative infinity.

In the case of the function y = 1/x, as x approaches positive or negative infinity, the value of y approaches 0. Therefore, the graph of the function has a horizontal asymptote at y = 0.

Other functions may have different horizontal asymptotes, depending on their behavior as x approaches positive or negative infinity.

Answer:

The answer is 153

Step-by-step explanation:

You multiply 17 by 3 by 3.

The volume of a rectangular prism-shaped freight container is calculated by multiplying its length, width, and height. For a container that is 17 meters long, 3 meters wide, and 3 meters high, the volume is 153 cubic meters.

The question is asking for the volume of the rectangular prism-shaped freight container.  In mathematics, the volume of a rectangular prism is found by multiplying its length, width, and height. For the freight container with dimensions of 17 meters long, 3 meters wide, and 3 meters high, we can find the volume by multiplying all these values together.

So, the volume V = length x width x height = 17m x 3m x 3m = 153 cubic meters. Therefore, each freight container on the train has a volume of 153 cubic meters.

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Answer:

Time t = 2 seconds

It will reach the maximum height after 2 seconds

Completed question;

Amir stands on a balcony and throws a ball to his dog who is at ground level. The ball's height, in meters above the ground, after t seconds that Amir has thrown the ball is given by:

H (t) = -(t-2)^2+9

many seconds after being thrown will the ball reach its maximum height?

Step-by-step explanation:

The equation of the height!

h(t) = -(t-2)^2 + 9 = -(t^2 -4t +4) + 9

h(t) = -t^2 +4t -4+9

h(t) = -t^2 + 4t +5

The maximum height is at dh/dt = 0

dh/dt = -2t +4 = 0

2t = 4

t = 4/2 = 2

Time t = 2 seconds

It will reach the maximum height after 2 seconds

The ball hits the ground at [tex]\( t = 5 \)[/tex] seconds.

Let's analyze the given height function of the ball:

[tex]\[ H(t) = -(t-2)^2 + 9 \][/tex]

This function describes the height of the ball [tex]\( H \)[/tex] in meters at any time [tex]\( t \)[/tex] in seconds.

The function is in the vertex form of a quadratic equation, which is generally written as:

[tex]\[ H(t) = a(t - h)^2 + k \][/tex]

Here, [tex]\( a = -1 \), \( h = 2 \), and \( k = 9 \).[/tex]

Time When the Ball Hits the Ground

- The ball hits the ground when [tex]\( H(t) = 0 \):[/tex]

[tex]\[ 0 = -(t-2)^2 + 9 \] \\\ (t-2)^2 = 9 \][/tex]

 Taking the square root of both sides:

[tex]\[ t-2 = \pm 3 \\\ t = 2 + 3 \quad \text{or} \quad t = 2 - 3 \\\ t = 5 \quad \text{or} \quad t = -1 \][/tex]

 Since negative time doesn't make sense in this context, we discard [tex]\( t = -1 \):[/tex]

[tex]\[ t = 5 \, \text{seconds} \][/tex]

 Therefore, the ball hits the ground at [tex]\( t = 5 \)[/tex] seconds.

The complete question is:

Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by: h(x)=-(x-2)^2+16 How many seconds after being thrown will the ball hit the ground?

Hello!

[tex]\boxed{ \bf Each~side~is~4~in~long.}[/tex]

We know that the formula for volume of a cube is:

V = a³

64 = a³

To find the side length, all we have to do is find the cube root of both sides.

[tex]\sqrt{64} = \sqrt{a^3}[/tex]

  4  =  a

Answer: 1) 390625, 2) 1365, 3) 411105.

Step-by-step explanation:

Since we have given that

Number of types of cupcakes = 5

Number of chocolate type = 1

1/ How many different selections of 8 cupcakes are there?

Number of cupcakes we need to select = 8

Since we have 5 options for each 8 cupcakes.

So, the number of ways to select 8 cupcakes would be :

[tex]5^8=390625[/tex]

2/ How many different selections of 8 cupcakes have at least 3 chocolate cupcakes?

Number of different selection would be :

=[tex]4^5+4^4+4^3+4^2+4+1=1365[/tex]

3/ How many different selections of 8 cupcakes have at most 2 chocolate cupcakes?

Number of ways to select no chocolate + Number of ways to select 1 chocolate + Number of ways to select 2 chocolate

[tex]5^8+4^7+4^6=411105[/tex]

Hence, 1) 390625, 2) 1365, 3) 411105.

Step-by-step explanation:

1.)

[tex] - \frac{5}{3} \times \frac{1}{8} = - \frac{5}{24} \\ \\ [/tex]

2.)

[tex] - \frac{5}{2} \times \frac{1}{12} = - \frac{5}{24} \\ [/tex]

3.)

[tex] - \frac{1}{6} \times \frac{5}{4} = - \frac{5}{24} \\ [/tex]

Answer: 6.07 I believe

Step-by-step explanation:

Answer:

-6.07

Step-by-step explanation:

What is the absolute magnitude of a star that has a period of 50 days?

Answer:

[tex]z=\frac{0.52 -0.64}{\sqrt{\frac{0.64(1-0.64)}{100}}}=-2.5[/tex]  

The p value for this case is given by:

[tex]p_v =2*P(z<-2.5)=0.0124[/tex]  

Step-by-step explanation:

Data given and notatio  

n=100 represent the random sample selected

X=52 represent the shoppers stating that the supermarket brand was as good as the national brand

[tex]\hat p=\frac{52}{100}=0.52[/tex] estimated proportion of stating that the supermarket brand was as good as the national brand

[tex]p_o=0.64[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of shoppers stating that the supermarket brand was as good as the national brand is 0.64 or not, then the system of hypothesis are.:  

Null hypothesis:[tex]p=0.64[/tex]  

Alternative hypothesis:[tex]p \neq 0.64[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Calculate the statistic  

The statistic is given by:

[tex]z=\frac{0.52 -0.64}{\sqrt{\frac{0.64(1-0.64)}{100}}}=-2.5[/tex]  

Statistical decision  

The p value for this case is given by:

[tex]p_v =2*P(z<-2.5)=0.0124[/tex]  

Answer:

a) 40 feet

b) 54 ft/min

c) 4 mins

Step-by-step explanation:

Solution:-

- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.

- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:

                           h ( t ) = −16t² + 54t + 40

Which gives the height of the baton from ground at time t mins.

- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.

- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:

                         h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40

                         h ( 0 ) = hi = 0 + 0 + 40 = 40 feet

Answer: The height of the platform hi is 40 feet.

- The speed ( v ) during the parabolic path of the baton also varies with time t.

- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.

                        v ( t ) = dh / dt

                        v ( t )= d ( −16t² + 54t + 40 ) / dt

                        v ( t )= -2*(16)*t + 54

                        v ( t )= -32t + 54

- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.

Hence,

                        v ( 0 ) = vi = -32*( 0 ) + 54

                        v ( 0 ) = vi = 54 ft / min

Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min

- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.

- The height of the ball at ground is zero. Hence,

                     h ( t ) = 0

                     0 = −16t² + 54t + 40

                     0 = -8t^2 + 27t + 20

- Use the quadratic formula to solve the quadratic equation:

                    [tex]t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t = \frac{27 + 37}{16} \\\\t = 4[/tex]

Answer: The time taken for the baton to hit the ground is t = 4 mins

Answer:

222.75 tons

Step-by-step explanation:

1 elephant = 8.25 tons

x 27               x 27

27 elephants = 222.75 tons

I hope this helps.

Final answer:

To find the weight of 27 elephants, multiply the weight of one elephant by 27. The total weight of 27 elephants, each weighing 8.25 tons, is 222.75 tons.

Explanation:

To calculate the total weight of 27 elephants each weighing 8.25 tons, we simply multiply the weight of one elephant by the number of elephants:

8.25 tons/elephant × 27 elephants = 222.75 tons

It's clear we need to multiply when converting from a single elephant's weight to the combined weight of multiple elephants. We use the fact that 1 ton = 2,000 pounds for conversion between units if needed, but here we keep the weight in tons as the question requested.

Answer:

1 43/100

Step-by-step explanation:

10 boys divide 7 cereal bars equally or

10 / 7 = 1.428571428571429

Or 1.43 rounded Or 1 43/100

Answer:

Medicare!

Step-by-step explanation:

Answer:

Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 11.3%  

Alternate Hypothesis, [tex]H_A[/tex] : p > 11.3%

Step-by-step explanation:

We are given that U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions.

Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership.

Let p = % of U.S. workers belonging to union membership

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 11.3%  

Alternate Hypothesis, [tex]H_A[/tex] : p > 11.3%

Here, null hypothesis states that the union membership has decreased or remained same in 2014.

On the other hand, alternate hypothesis states that the union membership has increased in 2014.

Also, The test statistics that will be used here is One-sample z proportion statistics;

                               T.S.  = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

Hence, the above hypothesis is appropriate that can be used to determine whether union membership increased in 2014.

Answer:

1

Step-by-step explanation:

We are given that an expression

[tex]{(-14)^0)^{-2}[/tex]

We have to find the value of given expression.

We know that

[tex]a^0=1[/tex]

Using the property

[tex](-14)^0=1[/tex]

We know that

[tex]a^{-b}=\frac{1}{a^b}[/tex]

Using the property

[tex](1)^{-2}=\frac{1}{1^2}[/tex]

[tex](1)^{-2}=1[/tex]

[tex]((-14)^0)^{-2}=1[/tex]

Answer:105°

Step-by-step explanation:

The intersecting chords form a pair of vertical angles.

Given is a circle, with chords AB and CD intersecting at E and m∠DEB = 105°, we need to find, m∠AEC

By vertical angle theorem:

Vertically opposite angles are congruent.

⇒ m∠AEC = m∠DEB

⇒ m∠AEC = 105°

The measure of angle AEC is 105°.

Therefore, the intersecting chords form a pair of vertical angles.

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Answer:

test statistics = 11.57

Step-by-step explanation:

test statics = [tex]\frac{average spend from the sample - average spend from theory}{Standard deviation / \sqrt{no of samples} }[/tex]

= [tex]\frac{115-100}{41/\sqrt{1000} }[/tex]  = 11.57

Answer:

1.) We cannot say for certain which candidate will win. But A has a statistical edge.

2.) We can say certainly that candidate A will win the election; albeit with a not so big margin.

3.) Candidate A will win this election based on the results of the final poll's before the election.

4.) We cannot say for certain which candidate will win. But A has a statistical edge.

The reasons are explained below.

Step-by-step explanation:

Confidence interval expresses a range of values in the distribution where the true proportion or mean can be found with some level of confidence.

Confidence Interval = (Sample Mean or Proportion) ± (Margin of error)

1. Candidate A: 54% & Candidate B:46% with Margin of error: + 5%

The confidence interval for candidate A

(54%) ± (5%) = (49%, 59%)

The confidence interval for candidate B

(46%) ± (5%) = (41%, 51%)

Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.

2. Candidate A: 52% & Candidate B:48% with Margin of error: + 1%

The confidence interval for candidate A

(52%) ± (1%) = (51%, 53%)

The confidence interval for candidate B

(48%) ± (1%) = (47%, 49%)

Here, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. So, candidate A wins this one, easily; albeit with a close margin though.

3. Candidate A: 53% & Candidate B:47% with Margin of error: + 2%

The confidence interval for candidate A

(53%) ± (2%) = (51%, 55%)

The confidence interval for candidate B

(47%) ± (2%) = (45%, 49%)

Here too, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. Hence, statistics predicts that candidate A wins this one.

4. Candidate A: 58% & Candidate B:42% with Margin of error: + 10%

The confidence interval for candidate A

(58%) ± (10%) = (48%, 68%)

The confidence interval for candidate B

(42%) ± (10%) = (32%, 52%)

Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.

Hope this Helps!!!

Answer:

The probability it will weigh between 2.95 and 3.1 ounces is 0.8186.

Step-by-step explanation:

We are given that Whitney Gourmet Cat Food has determined the weight of their cat food can is normally distributed with a mean of 3 ounces and a standard deviation of 0.05 ounces.

Let X = weight of their cat food can

So, X ~ Normal([tex]\mu=3,\sigma^{2} =0.05^{2}[/tex])

The z score probability distribution for normal distribution is given by;

                                Z =  [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 3 ounces

            [tex]\sigma[/tex] = standard deviation = 0.05 ounces

Now, the probability it will weigh between 2.95 and 3.1 ounces is given by = P(2.95 ounces < X < 3.1 ounces)

P(2.95 ounces < X < 3.1 ounces) = P(X < 3.1 ounces) - P(X [tex]\leq[/tex] 2.95 ounces)

   P(X < 3.1 ounces) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{3.1-3}{0.05}[/tex] ) = P(Z < 2) = 0.97725

    P(X [tex]\leq[/tex] 2.95 ounces) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{2.95-3}{0.05}[/tex] ) = P(Z [tex]\leq[/tex] -1) = 1 - P(Z < 1)

                                                              = 1 - 0.84134 = 0.15866

The above probabilities is calculated by looking at the value of x = 2 and x = 1 in the z table which has an area of 0.97725 and 0.84134 respectively.

Therefore, P(2.95 ounces < X < 3.1 ounces) = 0.97725 - 0.15866 = 0.8186

Hence, the probability it will weigh between 2.95 and 3.1 ounces is 0.8186.

Answer:

32.40

Step-by-step explanation:

Answer:

The statement is True.

Step-by-step explanation:

In this case we need to determine whether the rubber bands in a package of a particular brand of rubber band can hold a weight of 7 lbs or less.

A one-sample test can be used to perform the analysis.

The hypothesis can be defined as follows:

H₀: The mean weight the rubber bands can hold is 7 lbs, i.e. μ = 7.

Hₐ: The mean weight the rubber bands can hold is less than 7 lbs, i.e. μ < 7.

The information provided is:

 [tex]n=36\\\bar x=6.6\ \text{lbs}\\\sigma=2\ \text{lbs}[/tex]

As the population standard deviation is provided, we will use a z-test for single mean.

Compute the test statistic value as follows:

[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{6.6-7}{2/\sqrt{36}}=-1.20[/tex]  

The test statistic value is -1.20.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

 [tex]p-value=P(Z<-1.20)=0.1151[/tex]

*Use a z-table for the probability.

The p-value of the test is 0.1151.

The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.

Thus, it can be concluded that the mean weight the rubber bands can hold is 7 lbs.

Hence, the statement is True.