A coach of a baseball team orders hats for the 12 players on his team. Each hat costs $9.95. The shipping charge for the entire order is $5.00. There is no tax on the order. What is the total cost of the coach’s order ?

Answer:

no solutions

because it

Step-by-step explanation:

Question:

Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 1,000,000 and whose population proportion with a specified characteristic is p = 0.44 . Complete parts​ (a) through​ (c) below.

​(a) Describe the sampling distribution of ModifyingAbove p with caret.

A.)Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002

B.)Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0005

C.)Approximately​ normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0157

​(b) What is the probability of obtaining xequals480 or more individuals with the​ characteristic?

​P(xgreater than or equals480​)equals

nothing ​(Round to four decimal places as​ needed.)

​(c) What is the probability of obtaining xequals410 or fewer individuals with the​ characteristic?

​P(xless than or equals410​)equals

nothing ​(Round to four decimal places as​ needed.)

Answer:

a) Option C.

b) 0.1021

c) 0.0280

Step-by-step explanation:

Given:

Sample size, n = 1000

p' = 0.44

a) up' = p' = 0.44

The sampling distribution will be:

[tex] \sigma _p' = \sqrt{\frac{p' (1 - p')}{n}}[/tex]

[tex] = \sqrt{\frac{0.44 (1 - 0.44)}{1000}}[/tex]

[tex] = \sqrt{\frac{0.44*0.56}{1000}} = 0.0157 [/tex]

Option C is correct.

b) The probability when x ≥ 460

[tex] P' = \frac{x}{n} = \frac{460}{1000} = 0.46[/tex]

p'(P ≥ 0.46)

[tex] 1 - P = \frac{(p' - up')}{\sigma _p'} < \frac{0.46 - 0.44}{0.0157} [/tex]

[tex] = 1-P( Z < 1.27) [/tex]

From the normal distribution table

NORMSDIST(1.27) = 0.898

1-0.8979 = 0.1021

Therefore, the probability = 0.102

c) x ≤ 410

[tex] P' = \frac{x}{n} = \frac{410}{1000} = 0.41[/tex]

p'(P ≤ 0.41)

[tex] P = \frac{(p' - up')}{\sigma _p'} < \frac{0.41 - 0.44}{0.0157} [/tex]

[tex] = P( Z < - 1.9108) [/tex]

From the normal distribution table

NORMSDIST(-1.9108) = 0.0280

Probability = 0.0280

Answer:

P(N = n) = [tex](1-P)^{n-1} \times P[/tex]  

Step-by-step explanation:

to find out

Find the PMF PN (n)

solution

PN (n)

here N is random variable

and n is the number of times

so here N random variable is denote by the same package that is N (P)

so here

probability of N is

P(N ) = Ф ( N = n)          ..................  1

here n is = 1, 2,3, 4,...................... and so on

so that here P(N = n) will be

P(N = n) = [tex](1-P)^{n-1} \times P[/tex]  

Answer:

The growth rates at t = 0 is 8⁵.

The growth rates at t = 4 is 0.

The growth rates at t = 8 is -8⁵.

Step-by-step explanation:

The expression representing the size of the population at time t​ hours is:

[tex]b(t)=8^{6}+8^{5}t-8^{4}t^{2}[/tex]

Differentiate b (t) with respect to t to determine the growth rate as follows:

[tex]\frac{db(t)}{dt}=\frac{d}{dt} (8^{6}+8^{5}t-8^{4}t^{2})[/tex]

       [tex]=0+8^{5} (1)-8^{4}(2t)\\=8^{4}(8-2t)[/tex]

The growth rate is:

R (t) = 8⁴ (8 - 2t)

Compute the growth rates at t = 0 as follows:

[tex]R (0) = 8^{4} (8 - 2\times 0)\\=8^{4}\times 8\\=8^{5}[/tex]

Thus, the growth rates at t = 0 is 8⁵.

Compute the growth rates at t = 4 as follows:

[tex]R (4) = 8^{4} (8 - 2\times 4)\\=8^{4}\times 0\\=0[/tex]

Thus, the growth rates at t = 4 is 0.

Compute the growth rates at t = 8 as follows:

[tex]R (4) = 8^{4} (8 - 2\times 8)\\=8^{4}\times (-8)\\=-8^{5}[/tex]

Thus, the growth rates at t = 8 is -8⁵.

The growth rates at t=0 hours, t=4 hours, and t=8 hours can be calculated using the given equation.

When a bactericide is added to a nutrient broth in which bacteria are​ growing, the bacterium Population Growth in Bacteria continues to grow for a​ while, but then stops growing and begins to decline.

The size of the population at time t​ (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2.

Find the growth rates at t equals 0 hours commat=0 hours, t equals 4 hours commat=4 hours, and t equals 8 hours.t=8 hours.

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The probable question may be:

When a bactericide is added to a nutrient broth in which bacteria are​ growing, the bacterium population continues to grow for a​ while, but then stops growing and begins to decline. The size of the population at time t​ (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2. Find the growth rates when

t equals 0 hours commat=0 hours,

t equals 4 hours commat=4 hours,

t equals 8 hours.t=8 hours.

Answer:

Less

Step-by-step explanation:

10 = 10

1/2 < 3/4

1/2 = 50%

3/4 = 75%

Answer:

10 1/2 is less than 10 3/4

Step-by-step explanation:

10 1/2 is 10.5

10 3/4 is 10.75

Answer:

all of them are valid solutions

Step-by-step explanation:

So we plug in values of t below and get:

18 is < 107

54 is < 107

36 is < 107

27 is <107

Answer: 45

Step-by-step explanation:

Ok, Kid 1 can meet other 9 kids, so we have 9 handshaks.

Kid 2 can also meet other 9 kids, but he already meet kid 1, so we are not counting that handshake, this means that now we have 8 handshakes.

Kid 3 can also meet 9 kids, but we already counted the handshake with kid 1 and kid 2, so here we have other 7 andshakes.

And so on, so we have a total of:

9 + 8 + 7 + 6 + 5 + 4 +3 + 2 + 1 = 45 handshakes in total.

Answer:

45 handshakes

Step-by-step explanation:

Answer:

The point estimate is 0.45.

The 95% error margin is 0.042 = 4.2 percentage points.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Point estimate

We have that [tex]n = 540, x = 243[/tex]

So the point estimate is:

[tex]\pi = \frac{243}{540} = 0.45[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Error margin:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.45*0.55}{540}}[/tex]

[tex]M = 0.0420[/tex]

The 95% error margin is 0.042 = 4.2 percentage points.

Answer:

Probability that at least 1 of those sampled have access to on-line services at home is 0.9648.

Step-by-step explanation:

We are given that current estimates suggest that 20% of people with home-based computers have access to on-line services.

Suppose that 15 people with home-based computers were randomly and independently sampled.

The above situation can be represented through binomial distribution;

[tex]P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,3,......[/tex]

where, n = number of trials (samples) taken = 15 people

            r = number of success = at least one

            p = probability of success which in our question is % of people

                   who have access to on-line services at home, i.e.; p = 20%

Let X = Number of people who have access to on-line services at home

So, X ~ Binom(n = 15, p = 0.20)

Now, probability that at least 1 of those sampled have access to on-line services at home is given by = P(X [tex]\geq[/tex] 1)

           P(X [tex]\geq[/tex] 1) =  1 - P(X = 0)

                        =  [tex]1- \binom{15}{0}\times 0.20^{0} \times (1-0.20)^{15-0}[/tex]

                        =  [tex]1- (1\times 1 \times 0.80^{15})[/tex]

                        =  1 - 0.0352 = 0.9648

Hence, the required probability is 0.9648.

The following problem can be solved using the binomial distribution.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

There is 96.481% chance that at least 1 of those sampled have access to online services at home.

Substituting the values in a binomial distribution,

[tex]P(x\geq 1) = 1- P(0)[/tex]

[tex]P(x\geq 1) = 1-\ ^{15}C_0\times [0.20^0]\times [0.80^{(15-10)}]\\\\ P(x\geq 1)=1-\ 0.032\\\\ P(x\geq 1) = 0.96481\\\\ [/tex]

Hence, there is 96.481% chance that at least 1 of those sampled have access to online services at home.

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Answer:

45π or 141.4 [tex]cm^{3}[/tex]

Step-by-step explanation:

The volume of a cone is [tex]V=\frac{1}{3} \pi r^{2} h[/tex]

Here we have a diameter of 6 cm which means we have a radius of 3 (dividing by 2)

Our height here is 15 cm

Plugging in all our values we get [tex]\frac{1}{3}\pi[/tex][tex](3)^{2} (15)[/tex] which gives us 45π or 141.4 [tex]cm^{3}[/tex]

Answer:

if the side length of a cube = 6, then the surface area of the cube is:

36 + 36 + 36 + 36 + 36 + 36

Step-by-step explanation:

A cube has 6 faces.

so you have to add the faces 6 times to get the total surface area of a cube.

Answer:

The sum of 10.15 + 31.60 + 34.75 + 40 + 69.25 + 54.75 equals to 185.75

Step-by-step explanation:

10.15 + 31.6 + 34.75 + 40 + 69.25

        = 41.75 + 104 + 40

            = 145.75 + 40

                = 185.75

Alternate forms:

743/4 , 185 3/4

\frac{743}{4} 185\frac{3}{4}

Answer:

240.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

I have reproduced and attached a diagram (in figure 1) of the problem.

For ease of understanding, I have attached a second diagram which is labelled.

On line a

17+<CBE=180 (Linear Pair Postulate)

m<2=<CBE=180-17=163 degrees

<ABG=<CBE=163 degrees (Vertically Opposite Angles)

<ABE=<GBC= 17 degrees(Vertically Opposite Angles)

On line b

m<1=<DEB=<ABG=163 degrees (Corresponding Angles)

<BEF=<GBC= 17 degrees (Corresponding Angles)

<HEF=<DEB=163 degrees  (Vertically Opposite Angles)

<DEH=<BEF=17 degrees (Vertically Opposite Angles)

Therefore:

Answer:

Sample response: Angle 2 is a supplementary angle with 17°, so m∠2 = 163°. Since ∠1 and ∠2 are alternate interior angles of parallel lines, they are congruent, and the m ∠1 = m ∠2. Thus, m∠1 = 163°.

Step-by-step explanation:

PLZ GIVE BRAINLIEST!!!!!!!!!!!!!

Answer: jon & jim painted 8/12 of the fence

Step-by-step explanation: first, convert. one quarter is equal to 1/4, & 1/4 of 12 (since Jim painted 5/12) is 3/12. now we know that Jon painted 3/12 of the fence & that Jim painted 5/12 of the fence (we already knew this, didn't we?). all you have to do now is add: 3/12 + 5/12 = 8/12. so, jon & jim painted 8/12 of the fence.

- hope this helps

:)

Jon and Jim painted a total of two thirds of the fence together. We found this by converting 1/4 to 3/12 and then adding it to 5/12, which gave us 8/12, or 2/3.

The question involves understanding the addition of fractions. Jon painted a quarter of the fence which is equal to 1/4 and Jim painted five twelfths of the fence which is equal to 5/12.

To find out how much of the fence they painted together, we simply add these fractions. The lowest common multiple of 4 and 12 is 12. So, we convert 1/4 to 3/12 to make the denominators the same. Now, we have 3/12 (Jon's part) and 5/12 (Jim's part). The total part of the fence they painted together is 3/12 + 5/12 = 8/12 = 2/3.

So, Jon and Jim painted two thirds of the fence together.

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Answer:

A

Step-by-step explanation:

Our equation is: 9² + 2[(5 + 2)² - 4]. We need to use PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction.

The first thing to do is to add the 5 and 2 in the parentheses:

9² + 2[(5 + 2)² - 4]

9² + 2[(7)² - 4]

Then square the 7:

9² + 2[(7)² - 4]

9² + 2[49 - 4]

Do the subtraction operation within the parentheses/brackets:

9² + 2[49 - 4]

9² + 2[45]

Square 9:

9² + 2[45]

81 + 2[45]

Multiply 2 by 45:

81 + 2[45]

81 + 90

Thus, the answer is A.

Answer:

A

Step-by-step explanation:

9² + 2[(5+2)² - 4]

81 + 2[(7)² - 4]

81 + 2[49 - 4]

81 + 2(45)

81 + 90

Answer:

4 [tex]\frac{1}{2}[/tex]

OR

[tex]\frac{9}{2}[/tex]

Step-by-step explanation:

I'm not exactly sure which type of fraction you're asking for, so I'll put both.

This would be the fraction for 4.5 because the 0.5 is half of 1, while we already have a whole number, being 4.

OR

9 divided by 2 is 4.5, making the fraction for 4.5, [tex]\frac{9}{2}[/tex]

Answer:

9/2

Step-by-step explanation:

Answer:

3.3

Step-by-step explanation:

[tex] = > \frac{4 \frac{2}{5} }{1 \frac{1}{3} } \\ \\ = > \frac{ \frac{20 + 2}{5} }{ \frac{3 + 1}{3} } \\ \\ = > \frac{ \frac{22}{5} }{ \frac{4}{3} } \\ \\ = > \frac{22}{5} \times \frac{3}{4} \\ \\ = > \frac{11}{5} \times \frac{3}{2} \\ \\ = > \frac{33}{10} \\ \\ = > 3.3[/tex]

Answer:

a) 0.23

b) The 95% confidence interval for the population proportion is (0.1717, 0.2883).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Point estimate

The point estimate is:

[tex]\pi = \frac{46}{200} = 0.23[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.23 - 1.96\sqrt{\frac{0.23*0.77}{200}} = 0.1717[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.23 + 1.96\sqrt{\frac{0.23*0.77}{200}} = 0.2883[/tex]

The 95% confidence interval for the population proportion is (0.1717, 0.2883).

Answer:

The y intercept is (0,-22)

Step-by-step explanation:

To find the y intercept, set x =0 and solve for y

f(0)=-0^2+10*0-22

    = -22

Final answer:

To find the y-intercept of a quadratic function, substitute x = 0 into the function and calculate the value. In this case, the y-intercept of the function [tex]f(x) = -x^2 + 10x - 22[/tex] is at y = -22.

Explanation:

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, and it occurs when x = 0. To find the y-intercept of the quadratic function [tex]f(x) = -x^2 + 10x - 22[/tex], substitute x = 0 into the function.

Replace x with 0: f(0) =[tex]-(0)^2 + 10(0) - 22[/tex]

Calculate the value: f(0) = 0 + 0 - 22 = -22

Therefore, the y-intercept of the quadratic function is at y = -22.

Answer:

95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].

Step-by-step explanation:

We are given that the average half-life to be 7.4 hours. Suppose the variance of half-life is known to be 0.16.

They take 50 people, administer a standard dose of the drug, and measure the half-life for each of these people.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                      P.Q. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample average half-life = 7.4 hours

            [tex]\sigma[/tex] = population standard deviation = [tex]\sqrt{0.16}[/tex] = 0.4 hour

            n = sample of people = 50

            [tex]\mu[/tex] = population mean

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                     of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] <

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                            = [ [tex]7.4-1.96 \times {\frac{0.4}{\sqrt{50} } }[/tex] , [tex]7.4+1.96 \times {\frac{0.4}{\sqrt{50} } }[/tex] ]

                                            = [7.29 , 7.51]

Therefore, 95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].

The length of this interval is = 7.51 - 7.29 = 0.22

[tex] \frac{5}{4 {k}^{2} } [/tex]

Answer:5/4k^2

Step-by-step explanation:

5k/6 x 3/2k^3

(5k x 3) ➗ (6 x 2k^3)

15k/12k^3=5/4k^2

Answer:

10

Step-by-step explanation:

Answer:

-10

Step-by-step explanation

By substituting -2 in for all the X's you have (-2)^2+2(-2)-10. After ths is simplified you have 4+(-4)-10. -4+4 =0 and 0-10= -10

Answer:

[tex]a_{3} = 405[/tex]

Step-by-step explanation:

A geometric sequence is based on the following equation:

[tex]a_{n+1} = ra_{n}[/tex]

In which r is the common ratio.

This can be expanded for the nth term in the following way:

[tex]a_{n} = a_{1}r^{n-1}[/tex]

In which [tex]a_{1}[/tex] is the first term.

In this question:

[tex]a_{1} = 3645, a_{6} = 15[/tex]

Applying the equation:

[tex]a_{6} = a_{1}r^{6-1}[/tex]

[tex]a_{6} = a_{1}r^{5}[/tex]

[tex]3645r^{5} = 15[/tex]

[tex]r^{5} = \frac{15}{3645}[/tex]

[tex]r^{5} = \frac{1}{243}[/tex]

[tex]r = \sqrt[5]{\frac{1}{243}}[/tex]

[tex]r = \frac{1}{3}[/tex]

So

[tex]a_{n} = 3645 \times (\frac{1}{3})^{n-1}[/tex]

[tex]a_{3} = 3645 \times (\frac{1}{3})^{3-1} = 405[/tex]

Answer: 4.067units.

Step-by-step explanation:

(a) The highlighted arc is the major arc. That is , it covers from G to I.

(b) The length of the major arc will be

πr0°/180 where the angle substended at the center by the highlighted arc is

360° - 127° ( the angles if the arc not highlighted)

= 233°

Though this radius of the circle was not given so we are going to find the arc length without necessarily defining the radius.

Arc length = π × r × 233°

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

180

= 3.142 × r × 233°

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

180

= 4.067runits.

The arc that is highlighted is the major arc

The measure of the highlighted arc is 4.067runits.

The formula for the length of major arc

πr0°/180

Without highlioghts the angles are

360° - 127°

= 233 degrees

Formula for lenght of arc Arc length = π × r × 233° / 180

= = 3.142 × r × 233° / 180

= 4.067runits.

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Answer:

He has to save his clients $75,000.

Step-by-step explanation:

$2,000 per month is 2*2,000 = $24,000

He eanrs a fixed rate of $18,000 per year. So in bonuses, he has to earn 24,000 - 18,000 = $6,000.

His bonuses are 8% of the money he saves his clients.

So this 8% must be $6,000. How much his 100%?

0.08 - $6,000

1 - $x

[tex]0.08x = 6000[/tex]

[tex]x = \frac{6000}{0.08}[/tex]

[tex]x = 75000[/tex]

He has to save his clients $75,000.

Answer:

5/24

Step-by-step explanation:

First, we want to get a common denominator, so we multiply them together.

The 2 new fractions are. . .

4/24 (1/6) and 6/24 (1/4)

Now, if you are looking for the number between 4/24 and 6/24, the answer is 5/24.

Answer:

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that​ parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

We have to see if 50% = 0.5 is part of the confidence interval.

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1095, \pi = \frac{478}{1095} = 0.4365[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 - 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4118[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 + 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4612[/tex]

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that​ parents' attitudes toward the quality of education have changed.

After a blue marble is drawn and not replaced, the probability of drawing a red marble from the bag containing initially 28 red and 22 blue marbles is 9/16.

The question is asking for the probability of picking a red marble after a blue marble has been picked first and not replaced. The bag originally contains 50 marbles, 28 red ones, and 22 blue ones. After removing one blue marble, there would be 27 red marbles and 21 blue ones left, making a total of 48 marbles.

To find the probability of now drawing a red marble, we divide the number of red marbles by the new total number of marbles:

Probability = Number of Red Marbles / Total Number of Marbles

Probability = 27 / 48

Probability = 9 / 16

Therefore, the probability of drawing a red marble after having already drawn a blue marble and not replacing it is 9/16.

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Answer:

We conclude that the treatment does not has a significant effect.

Step-by-step explanation:

We are given that to evaluate the effect of a treatment, a sample (n = 16) is obtained from a population with a mean of µ = 30 and a treatment is administered to the individuals in the sample.

After treatment, the sample mean is found to be M = 31.3 with a sample standard deviation of s = 3.

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30      {means that the treatment does not has a significant effect}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 30      {means that the treatment has a significant effect}

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

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

where, M = sample mean = 31.3

             s = sample standard deviation = 3

             n = sample size = 16

So, test statistics  =  [tex]\frac{31.3-30}{\frac{3}{\sqrt{16}}}[/tex]  ~ [tex]t_1_5[/tex]

                              =  1.733

The value of t test statistics is 1.733.

Now, at 0.05 significance level the t table gives critical values of -2.131 and 2.131 at 15 degree of freedom for two-tailed test. Since our test statistics lie within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the treatment does not has a significant effect.

The data are not sufficient to conclude that the treatment has a significant effect. The calculated test statistic is less than the critical value for a two-tailed test with a significance level of α = 0.05, hence we fail to reject the null hypothesis.

To determine if the treatment had a significant effect, we must conduct a hypothesis test. This falls under the field of statistics.

First, let's state our null hypothesis (H₀) and alternative hypothesis (H₁). H₀: µ = 30 (i.e., the treatment has no effect) and H₁: µ ≠ 30 (treatment has an effect).

Next, we find the standard error (SE) of the mean, which is s/√n = 3/√16 = 0.75.

We then calculate our test statistic, which is the difference between M (sample mean) and µ (population mean) divided by the SE: (31.3 - 30) / 0.75 = approximately 1.73.

Given a two-tailed test with a significance level of α = 0.05, the critical z-values would be -1.96 and +1.96. As our calculated test statistic falls between these two critical values (-1.96reject the null hypothesis.

Consequently, the data are not sufficient to conclude that the treatment has a significant effect.

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