A company mixes pecans, cashews, peanuts, and walnuts to make a batch of mixed nuts.
About 15.4% of the mixed nuts in a batch are pecans.
If a batch contains 77 pounds of pecans, how many pounds of mixed nuts are in a batch altogether?

Answer:

15/56

Step-by-step explanation:

Total = 8

3/8 × 5/7

15/56

Answer:

  7 is located to the right of -2

Step-by-step explanation:

Larger numbers are to the right on a number line, so the statement that 7 is larger than -2 means ...

  7 is located to the right of -2

Answer:

[tex]t=\frac{18.7-20}{\frac{5}{\sqrt{80}}}=-2.326[/tex]    

[tex]df=n-1=80-1=79[/tex]  

[tex]p_v =P(t_{(79)}<-2.326)=0.0113[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X=18.7[/tex] represent the sample mean for the content of active ingredient

[tex]s=5[/tex] represent the sample standard deviation for the sample  

[tex]n=80[/tex] sample size  

[tex]\mu_o =20[/tex] represent the value that we want to test

t would represent the statistic

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

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean for the active agent is at least 20 mg, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 20[/tex]  

Alternative hypothesis:[tex]\mu < 20[/tex]  

The statistic would be:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Now we can calculate the statistic:

[tex]t=\frac{18.7-20}{\frac{5}{\sqrt{80}}}=-2.326[/tex]    

P value

The degrees of freedom are calculated like this:

[tex]df=n-1=80-1=79[/tex]  

Since is a one left tailed test the p value would be:  

[tex]p_v =P(t_{(79)}<-2.326)=0.0113[/tex]  

Option (e) 0.0113 is correct. The approximate p-value for the lab's one-sample t-test on fluoxetine is 0.0113.

To determine the approximate p-value for the lab's test on fluoxetine, we can use a one-sample t-test. Here's a step-by-step explanation:

(bar{x} - μ) / (s/√n)

where bar{x} is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

bar{x} = 18.7, μ = 20, s = 5, n = 80

t = (18.7 - 20) / (5/√80)

t = -1.3 / (5/8.944)

t = -1.3 / 0.559

t = -2.325

Therefore, the correct answer is e. 0.0113.

Complete question:

Fluoxetine, a generic anti-depressant, claims to have, on average, at least 20 milligrams of active ingredient. An independent lab tests a random sample of 80 tablets and finds the mean content of active ingredient in this sample is 18.7 milligrams with a standard deviation of 5 milligrams. If the lab doesn't believe the manufacturer's claim, what is the approximate p-value for the suitable test?

a. 0.0226

b. 0.4885

c. 0.5115

d. 0.15

e. 0.0113

Answer:

  y = -2

Step-by-step explanation:

The equation of a horizontal line is ...

  y = constant

In order to make it go through a point with a y-coordinate of -2, the value of the constant must be -2.

Your line is y = -2.

Answer:

1. There are 648 total combinations that can be chosen.

2. After she choses two possiblilities the total number changes to 108 total posibilities to chose from

Step-by-step explanation:

possibility: 1/2 x 1/3 x 1/2 x 1/6 x 1/9 = 648

then you remove the first two because she chose those ones

1/2 x 1/6 x 1/9 = 108 possibilities left

Answer:

Step-by-step explanation:

1.       C

2.        C

3.         B

Answer:

The model car is 10 inches long

Step-by-step explanation:

To solve this question, we use conversion of units

Feet to inches.

Each feet has 12 inches.

The car is 15ft long.

So the car has 15*12 = 180 inches.

.5 inches = 9 in.

Rule of three

.5 inches - 9 inches

x inches - 180 inches

[tex]9x = 180*0.5[/tex]

[tex]9x = 90[/tex]

[tex]x = \frac{90}{9}[/tex]

[tex]x = 10[/tex]

The model car is 10 inches long

To find the length of Uni's model car, we convert the actual car's length to inches, set up a proportion with the given scale, and cross-multiply to solve for the model car's length, resulting in a model that is 10 inches long.

The subject matter of the question is related to scale models, which falls under the field of Mathematics. To solve this problem, we need to find the length of the model car based on the given scale and the actual length of the car.

The scale given is 0.5 inches = 9 inches. Firstly, we need to convert the actual length of the car from feet to inches, so we can work in the same units. There are 12 inches in a foot, so a 15 feet long car is 15 x 12 inches long, which is 180 inches. Now, we need to set up a proportion to find the length of the model car:

Actual car length (inch) : Model car length (inch) = Actual scale (inch) : Model scale (inch) 180 inches (actual car length) : x inches (model car length) = 9 inches (actual scale) : 0.5 inches (model scale)

By cross-multiplying, we get:

(180 inches x 0.5 inches) = (x inches x 9 inches)

Dividing both sides by 9 inches, we get:

x inches = (180 inches x 0.5 inches) / 9 inches

So, the length of the model car is:

x inches = 10 inches.

Therefore, Uni's model car is 10 inches long.

Final answer:

None of the provided expressions have a greatest common factor of 3xy² with 42xy⁴ because they do not contain the necessary factors of 3, x, and y².

Explanation:

The student is asking for expressions that have a greatest common factor (GCF) of 3xy² with 42xy⁴. To find expressions with a GCF of 3xy², we need to look for expressions that include multiples of 3xy² in their factorization.

Looking at the provided expressions:

Therefore, none of the provided expressions have a GCF of 3xy² with 42xy⁴.

Answer:

12.

Step-by-step explanation:

Given that,

Number of while balls are 3

Number of green balls are 4

Number of red balls are 5

We need to find the total number of outcomes. We know the total number of outcomes in is number of choices.

In this case, total number of outcomes are the sum of all color balls i.e. 3 + 4 + 5 = 12 balls.

Hence, the total number of outcomes are 12.

Final answer:

The total number of outcomes when one ball is drawn at random from a bag containing 3 white, 4 green, and 5 red balls is 12.

Explanation:

A bag contains 3 white balls, 4 green balls, and 5 red balls. The total number of possible outcomes when a ball is drawn at random is simply the sum of all the balls in the bag. Since each ball can be selected in one distinct way, we calculate the total number of outcomes by adding the number of white balls, the number of green balls, and the number of red balls.

So, the total number of outcomes is:

3 (white) + 4 (green) + 5 (red) = 12 (total outcomes)

Therefore, there are 12 different possible outcomes when one ball is drawn at random from this bag.

Answer:

25 Inches

Step-by-step explanation:

Given the table:

[tex]\left|\begin{array}{c|c|c|c|c}\text{Number of Inches}&2&10&&40\\\text{Number of Centimeters}&5.08&25.04&63.5&101.6\end{array}\right|[/tex]

We want to determine the missing value on the table.

Let the missing value be x.

1 inch = 2.54 cm

x inch = 63.5

Expressing the above as a ratio

[tex]\dfrac{1}{x}=\dfrac{2.54}{63.5} \\$Cross Multiply$\\2.54x=63.5\\$Divide both sides by 2.54$\\x=25 \:Inches[/tex]

Therefore, the missing value is 25.

Answer:

25 Inches

Step-by-step explanation:

hope this helps :))

Answer:

90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

Step-by-step explanation:

We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.

Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;

                            P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average speed of cars = 70.7 miles per hour

             s = sample standard deviation = 6.3 miles per hour

             n = sample of cars = 37

             [tex]\mu[/tex] = true mean speed

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the true mean, [tex]\mu[/tex] is ;

P(-1.688 < [tex]t_3_6[/tex] < 1.688) = 0.90  {As the critical value of t at 36 degree of

                                 freedom are -1.688 & 1.688 with P = 5%}  

P(-1.688 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.688) = 0.90

P( [tex]-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

P( [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                    = [ [tex]70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] , [tex]70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] ]

                    = [68.9517 miles per hour , 72.4483 miles per hour]

Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.

Answer:

The answer to the nearest foot is = 15 feet

Step-by-step explanation:

Solution

The first set taken is to  Compute L for a 55-mph speed limit

Given that

L =(θ2 -θ1)/200 (h +S Tan ∝) =

= ( u + 5) 336²/200 (1.9 +336 tan 0.7°)

= 9° (336)²/200 (1.9 +336 tan 0.7°) = 14.7652094

= 15 feet  { 9° = 9*π/180 = π/20}

Note: Kindly find an attached image for the complete question given and answered

Answer:

i believe the answer is 1/27

Step-by-step explanation:

you take the fractions and multiply them all together.

1x1x1 equals 1

and 3x3x3 equals 27

meaning the answer is 1/27 :)

To calculate 1/3 x 1/3 x 1/3, you're effectively cubing 1/3, which results in (1/3)^3 or 1^3/3^3, simplifying to 1/27.

The student is asking about the multiplication of fractions and exponentiation rules in algebra. To solve 1/3 x 1/3 x 1/3, you multiply the fractions normally. When multiplying identical fractions, we simply raise the fraction to the power of the number of times it is being multiplied by itself. So 1/3 x 1/3 x 1/3 is equivalent to (1/3)^3. When you raise a fraction to an exponent, you raise both the numerator and the denominator to that power. Therefore, (1/3)^3 equals 1^3/3^3, which simplifies to 1/27.

The example given with 3².35 relates to the rules of exponents, which state that when multiplying exponential terms with the same base, you can add the exponents (x^p x x^q = x^(p+q)). For the concept of cubing of exponentials, you would cube the base and multiply the existing exponent by 3 to execute the operation effectively.

Answer:

A rectangle and a triangle

Step-by-step explanation:

Answer:

(-0.5,-2.5)

Step-by-step explanation:

(x1 + x2) / 2 = x midpoint

(y1 + y2) / 2 = y midpoint

x)

2 + -3 = 5

5 / 2 = -0.5

y)

4 + -9 = -5

-5 / 2 = -2.5

= (-0.5, -2.5)

The midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

We have to find the midpoint of A and B where A has coordinates (2, 4)

and B has coordinates (-3, -9).

Midpoint = (2-3/2, 4-9/2)

=(-1/2, -5/2)

Hence, the midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)

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Answer:

We conclude that the college students spend less time on extra-curricular activities than they did ten years ago.

Step-by-step explanation:

We are given that Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities.

A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours.

Let [tex]\mu[/tex] = average time spent on extra-curricular activities.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 120 hours     {means that the college students spend more or equal time on extra-curricular activities than they did ten years ago}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 120 hours     {means that the college students spend less time on extra-curricular activities than they did ten years ago}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                       T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average number of hours spent per semester = 107 hrs

             s = sample standard deviation = 45 hours

             n = sample of college students = 100

So, test statistics  =  [tex]\frac{107-120}{\frac{45}{\sqrt{100} } }[/tex]  ~  [tex]t_9_9[/tex]

                               =  -2.889

The value of t test statistics is -2.889.

Now, the P-value of the test statistics is given by following formula;

               P-value = P( [tex]t_9_9[/tex] < -2.889) = 0.00314

Since, the P-value is less than the level of significance as 0.05 > 0.00314, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the college students spend less time on extra-curricular activities than they did ten years ago.

Answer: gang in la

Step-by-step explanation:

Answer:

Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.

Step-by-step explanation:

Given that,

The diameter of cylindrical bucket = 12 in.

Depth is increasing at the rate of = 4.0 in per minutes.

i.e [tex]\frac{dh_1}{dt}=4[/tex]

[tex]h_1[/tex] is depth of the bucket.

The volume of the bucket is V = [tex]\pi r^2 h[/tex]

                                                 [tex]=\pi \times 6^2\itimes h_1[/tex]

[tex]\therefore V=36\pi h_1[/tex]

Differentiating with respect yo t,

[tex]\frac{dV}{dt}=36\pi \frac{dh_1}{dt}[/tex]

Putting  [tex]\frac{dh_1}{dt}=4[/tex]

[tex]\therefore\frac{dV}{dt}=36\pi\times 4[/tex]

The rate of volume change of the bucket = The rate of volume change of the aquarium .

Given that,The aquarium measures 24 in × 36 in × 18 in.

When the water pumped out from the aquarium, the depth of the aquarium only changed.

Consider h be height of the aquarium.

The volume of the aquarium is V= ( 24× 36 ×h)

V= 24× 36 ×h

Differentiating with respect to t

[tex]\frac{dV}{dt}=24\times 36 \times \frac{dh}{dt}[/tex]

Putting [tex]\frac{dV}{dt}=36\pi\times 4[/tex]

[tex]36\pi\times 4= 24\times 36\times \frac{dh}{dt}[/tex]

[tex]\Rightarrow \frac{dh}{dt}=\frac{36\pi \times 4}{24\times 36}[/tex]

[tex]\Rightarrow \frac{dh}{dt}=\frac{11}{21}[/tex]

Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.

To find the rate at which the aquarium water level is dropping, calculate the volume of water being pumped into the bucket per minute and the volume of the aquarium. Then, divide the volume of water by the volume of the aquarium to find the rate.

To find the rate at which the aquarium water level is dropping, we first need to determine the flow rate of water being pumped into the cylindrical bucket.

Now, let's find the rate at which the aquarium water level is dropping:

By calculating the above expression, you can find the rate at which the aquarium water level is dropping.

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The water level in the aquarium is dropping at an average rate of π/6 inches per minute. This is obtained by relating the volumes and their rates of change in both the bucket and the aquarium.

The subject of this question is calculus, specifically, related rates. The situation describes two rates: one at which the depth of water in the bucket is increasing, and one at which the water level in the aquarium is dropping - a classic related rates problem.

To comprehend this, let us calculate the volume rates of each one: the bucket and the aquarium. The bucket is referred as cylindrical with a radius of 6 inches (half of 12 inches). The volume of a cylinder is V = πr²h. The depth or height, h, is increasing at the rate of 4 inches per minute, so dh/dt = 4 in/min. The rate at which the volume has been changing, dV/dt = πr²dh/dt = π * (6 in)² * 4 in/min = 144π in³/min.

The aquarium is a rectangular prism, thus its volume can be calculated by V = l*w*h. Therefore, the rate at which the water level is dropping is dV/dt / (l*w) which equals 144π in³/min divided by the area of the aquarium (24in*36in = 864 in²), which gives dh/dt = 144π / 864, which reduces to dh/dt = π/6 in/min downwards. Hence, the water level in the aquarium is dropping at π/6 in/min on an average.

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Answer:

(a)[tex]\frac{7}{25}[/tex]

(b)[tex]\frac{19}{116}[/tex]

(c)[tex]\frac{28}{125}[/tex]

Step-by-step explanation:

Number of juniors who attended prom,n(J)=28

Number of seniors who attended prom,n(S)=97

Number of juniors who did not attend prom,n(J')=56

Number of seniors who did not attend prom,n(S')=19

(a) P (a junior who did not attend prom)

[tex]P(J')=\frac{56}{200}= \frac{7}{25}[/tex]

(b)

[tex]P(Senior)=\frac{116}{200}[/tex]

[tex]P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}[/tex]

(c)P (junior | attended prom)

[tex]P(Senior)=\frac{84}{200}[/tex]

[tex]P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}[/tex]

Answer:

A. P = 7/25

B. P = 19/116

C. P = 28/125

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly this way:

      Juniors  Seniors   Totals

Yes       28         97          125

No       56         19           75

Totals   84        116          200

2. Find the probability of each of the events.

Let's recall that the formula of probability is:

P = Number of favorable outcomes/Total number of possible outcomes

A. P (a junior who did not attend prom)

P = Juniors who did not attend prom/Total number of students surveyed

P = 56/200

P = 7/25 (Diving by 8 numerator and denominator)

B. P (did not attend prom | senior)

P = Seniors who did not attend prom/Total number of seniors surveyed

P = 19/116

C. P (junior | attended prom)

P = Juniors who attend prom/Total number of students attended prom

P = 28/125

Answer:

-4

Step-by-step explanation:

Each term is 4 less than the term before it, so the common difference is -4.

Answer:

B. -4 on edge !!

Step-by-step explanation:

Got it right :)

Answer:

$220262

Step-by-step explanation:

We are given that an exponential function

[tex]g(x)=190000\cdot(1.03)^x[/tex]

Where x=Number of years

We have to find the value of Evie's house after 5 years .

Substitute the values in the given function

[tex]g(5)=190000\cdot(1.03)^5[/tex]

[tex]g(5)=220262.07[/tex]

[tex]g(5)\approx 220262[/tex]

Hence, the value of Evie's house after 5 years=$220262

Final answer:

The question involves Mathematics and requires understanding of statistics and normal distribution to find z-scores for designing helmets to fit a specific range of male head breadths, accommodating all except the smallest and largest 4.3%.

Explanation:

The subject of this question is Mathematics, specifically focusing on statistics and the concept of normal distribution. Engineers designing helmets need to consider the breadths of male heads, which are normally distributed with a given mean and standard deviation. The design requirements stipulate that the helmets should fit all men except for those in the extremities of the distribution (smallest 4.3% and largest 4.3%).

To address such a problem, one would typically use the z-score to identify the cutoff points on a standard normal distribution that correspond to these percentages. The z-score represents the number of standard deviations a data point is from the mean. Therefore, the engineers must calculate the z-scores that correspond to the smallest and largest 4.3% of the distribution to determine the range of head breadths the helmets must accommodate.

Answer:

Weight of mixing water=224.541 lb

Step-by-step explanation:

Taking 1 cubic yard of concrete

Mass of gravel = 2314 lb

Moisture content = 3.5% Absorption 4.2%

Extra water needed = (4.2-3.5)*2314/100= 16.198 lb

Mass of sand= 899 lb

Moisture content = 5.7% Absorption =1.4%

Water released = (5.7-1.4)*899/100= 38.657 lb

Free water = 244 lb

Weight of mixing water = free water + extra water needed-water released = 244+16.198-38.657=224.541 lb

Weight of mixing water=224.541 lb

To calculate milk needed for a different number of pancakes and determine the amount of butter for a varied pancake quantity.

To calculate the amount of milk needed for 4 pancakes that Simon is making:

Divide the amount of milk needed for 8 pancakes (250ml) by 2 since 4 is half of 8. 250ml ÷ 2 = 125ml.

To determine the amount of butter for the 12 pancakes that Craig is making:

Since the recipe calls for 5g of butter for 8 pancakes, we can calculate the amount needed for 12 pancakes by setting up a proportion: (5g/8 pancakes) = (x/12 pancakes). Solving for x gives x = 7.5g.

Answer:

The calculated value z = 1.3145 < 2.326 at  0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

Step-by-step explanation:

Step(i):-

An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

The mean of the Population 'μ' = 28.0miles/gallon

Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.

The sample size 'n' = 270

Mean of the sample 'x⁻' = 27.8

Given Population variance 'σ² = 6.25

The standard deviation of Population 'σ' = √6.25 = 2.5

Step(ii):-

Null hypothesis :H₀: 'μ' = 28.

Alternative hypothesis :H₁: 'μ' ≠28.

The test statistic

[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{27.8-28 }{\frac{2.5}{\sqrt{270} } } = \frac{-0.2}{0.15214}[/tex]

Z = -1.3145

|Z| = |-1.3145|= 1.3145

Step(iii):-

The tabulated value  of z-score at 0.02 level of significance = 2.326

The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

Answer:

the answer is container c

b=11.14in2

12in

Step-by-step explanation:

Answer:

Answer is C

Step-by-step explanation:

Answer:

(y-12)/4

Step-by-step explanation:

If g(x) is the inverse of f(x)

and f(x) = 4x + 12

f⁻¹(x) = g(x)

let f(x) be represented as y

f(x) = y

y = 4x + 12

subtract 12 from both sides

y-12= 4x

divide both sides by 4

(y-12)/4 = x

so f  ⁻¹ (y)=  (y-12)/4 so g(x) =  (x-12)/4

Answer:

Barney 145 3 Days 310 Miles

Mary   250 5 Days 600 Miles

A)  3 D + 310 M = 145

B) 5 D + 600 M = 250

Multiplying A) by -5/3

A) -5 D - 516.6666M = -241.66666666

B) 5D + 600M = 250

Adding A) and B)

83.3333 M = 8.3333333333

M = .10 per mile

3 D = 114

Daily Rate = 38 dollars per day

Step-by-step explanation:

Answer:

0.3876<p<0.4389

Step-by-step explanation:

-Given [tex]n=2472, \ x=1022 , \ CI=0.99[/tex]

-We calculate the proportion of surveys returned:

[tex]\hat p=\frac{1022}{2472}\\\\=0.4134[/tex]

For a 99% confidence interval:

[tex]z_{\alpha/2}=2.576[/tex]

#The margin of error is calculated as;

[tex]ME=z_{0.005}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=2.576\times \sqrt{\frac{0.4134(1-0.4134)}{2472}}\\\\=0.0255[/tex]

The confidence interval are then:

[tex]CI=\hat p\pm ME\\\\=0.4134\pm 0.0255\\\\=[0.3876,0.4389][/tex]

Hence, the confidence interval is 0.3876<p<0.4389

The null hypothesis will be rejected if the test statistic is: greater than -2.33

The null hypothesis will be rejected if the test statistic falls within the critical region, which is determined by the significance level (0.01 in this case).

To determine the test statistic, calculate the z-score for the sample proportion and compare it to the critical value.

The formula to calculate the z-score for the sample proportion is:

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

Where:

[tex]\hat{p}[/tex] is the sample proportion (230/1189 = 0.193)

p is the population proportion (0.22)

n is the sample size (1189)

Calculating the z-score:

z = (0.193 - 0.22) / [tex]\sqrt[/tex](0.22 * (1 - 0.22) / 1189)

z = -2.25

To determine if the null hypothesis is rejected or not, compare the absolute value of the z-score to the critical value for a one-tailed test at a 0.01 significance level.

The critical value for a one-tailed test at a 0.01 significance level is approximately -2.33.

If the absolute value of the calculated z-score is greater than 2.33, we reject the null hypothesis.

Since absolute value of the calculated z-score is not greater than 2.33, null hypothesis is not rejected.

Answer:

The value of t test statistics is 4.518.

Step-by-step explanation:

We are given that director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds.

He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds.

Let [tex]\mu[/tex] = mean length of commercials on his station.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24 seconds     {means that the mean length of commercials on his station is equal to 24 seconds}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24 seconds     {means that the mean length of commercials on his station is different from 24 seconds}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                        T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average length of these commercials = 26.3 seconds

            s = sample standard deviation = 7.2 seconds

            n = sample of commercials = 200

So, test statistics  =  [tex]\frac{26.3-24}{\frac{7.2}{\sqrt{200} } }[/tex]  ~ [tex]t_1_9_9[/tex]  

                               =  4.518

The value of t test statistics is 4.518.