2. In a random sample of 100 people, the correlation between amount of daily exercise and weight was found to be –.21. What would be the likely effect on the absolute value of the correlation coefficient under the following circumstances? (Hint: would r be greater or smaller? Why?) a. The sample is restricted to people who weighed less than 180 pounds

Answer:

[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]

Step-by-step explanation:

Since it is circular slick, it's volume can be modeled as,

[tex]V = \pi R^{2}h[/tex]

Where R is the radius in feet and h is the thickness of slick.

taking derivative of the above equation with respect to time yields,

[tex]\frac{dV}{dt} = \pi 2Rh \frac{dR}{dt}[/tex]

Where the rate of change of radius of the slick (dR/dt) is given,

[tex]\frac{dV}{dt} = \pi 2(400)(0.2)(0.31)[/tex]

[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]

Therefore, the rate of change of volume is 155.82 cubic feet per minute.​

The value of dV/dt using pi almost equal to 3.14 gives; dV/dt = 155.82 ft³/min

dV/dt = 155.82 ft³/min

We are given;

Radius; R = 400 ft

Height; h = 0.2 ft

Rate of Increase of radius; dr/dt = 0.31 ft/min

Formula for Volume of a cylinder is;

V = πr²h

Differentiation of both sides of V and r with respect to t gives;

dV/dt = 2πrh(dr/dt)

Plugging in the relevant values gives;

dV/dt = 2π × 400 × 0.2 × 0.31

dV/dt = 155.82 ft³/min

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Answer: the average speed of the runners increased since last year.

Step-by-step explanation:

The table is:

                   Mean     MAD

Last Year    16.2 s     1.2

This Year    14.7 s      1.9

Looking at this table we can see that this year, the mean time is smaller than the one from last year, so the runners are faster in average.

The mean absolute deviation is bigger, but the change in the mean is bigger.

difference of the mean   16.2 - 14.7 = 1.5

difference of the MAD  1.9 - 1.2 = 0.7

This means that the average speed of the runners increased since last year, and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike like last year.

Answer:

this guy above me is a genuies it correct

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

200 men and 2,000 women

i dont know how but that was just the answer

The sampling distribution of ā-Ă will be approximately normal when both populations satisfy the conditions for np > 5 and nq > 5. The sample sizes must ensure these inequalities are met using the proportions 0.08 for men and 0.005 for women.

The sampling distribution of ā - Ă will be approximately normal when the sample sizes are large enough to satisfy the condition np > 5 and nq > 5 for both populations. Given that in the population of men, 8 percent carry the genetic trait (p1 = 0.08), and in the population of women, 0.5 percent carry the trait (p2 = 0.005), we need to find appropriate sample sizes for each population.

For the men's population:
n1p1 > 5 and n1(1 - p1) > 5.

For the women's population:
n2p2 > 5 and n2(1 - p2) > 5.

The sample sizes should be selected in a way that these inequalities are met for both populations to ensure that the sampling distribution of ā-Ă is approximately normal.

Answer:

The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.

Approximation at points (1.1,1.9) is 0.7

Step-by-step explanation:

Given:

Tangent plane to  a surface z=5x+2y-10 as the function at point (1,2)

To find :

f(x,y) at (1,2)

partial derivatives of function w.r.t. (x and y) and value of that function at given points.

Solution:(refer the attachment also)

Now we know that

the equation of tangent plane at given points to the surface is given by,

f(x1,y1,z1) and z=f(x,y)

z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)

here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.

now

taking partial derivative w.r.t. x we get

Fx(x1`,y1)=[tex]\frac{d}{dx} (5x+2y-10)[/tex]

=5.

Then w.r.t y we get

Fy(x1,y1)=

[tex]\frac{d}{dy}(5x+2y-10)[/tex]

=2.

The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.

Using the Linearization or linear approximation we get

L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)

=-1+5(x-1)+2(y-2)

=5x+2y-10

Approximation at F(1.1,1.9)

=5(1.1)+2(1.9)-10

=5.5+3.8-10

=0.7

Approximation at points (1.1,1.9) is 0.7

Final answer:

The partial derivatives of f(x, y) at (1, 2) are fx(1,2) = 5 and fy(1,2) = 2. The function value f(1,2) is 0. An approximation for f(1.1, 1.9) using the tangent plane is 0.5.

Explanation:

The question concerns the computation of partial derivatives and the evaluation of a function f(x, y) given its tangent plane at a specific point. Given the tangent plane to z=f(x,y) at the point (1, 2), which is z=5x+2y−10, we have:

fx(1,2) is the partial derivative of z with respect to x at the point (1,2), equivalent to the coefficient of x in the tangent plane equation, which is 5.

fy(1,2) is the partial derivative of z with respect to y at the point (1,2), equivalent to the coefficient of y in the tangent plane equation, which is 2.

To find f(1,2), we substitute x=1 and y=2 into the tangent plane equation to get z = 5(1) + 2(2) − 10 = 0.

The value f(1.1,1.9) can be approximated by using the tangent plane equation. By plugging x=1.1 and y=1.9 into the equation, we obtain z = 5(1.1) + 2(1.9) - 10 = 0.5, for an approximate value of f(1.1, 1.9).

Summary of Answers:

fx(1,2) = 5

fy(1,2) = 2

f(1,2) = 0

f(1.1,1.9) ≈ 0.5

The correlation is 0.824. The equation of the regression line is Y = -12.6 + 0.722X. The estimated verbal score for a math score of 387 can be calculated by inputting 387 in place of X in the regression equation.

The subject of this question is regression analysis, which is a type of statistical modeling technique.

A) The correlation, as given in the question, is 0.824. This number tells us the degree to which the math and verbal scores vary together.

B) The regression equation predicting verbal scores from math scores can be calculated as follows:

Regression line equation is Y = a + bX. 'a' is Y intercept, 'b' is the slope, 'X' is the value of the independent variable (in this case math scores), and 'Y' is the predicted value of the dependent variable (in this case, verbal scores). We calculate the slope 'b' using the formula b = r*(Sy/Sx), where r is the correlation coefficient, Sy is the standard deviation of Y (verbal scores) and Sx is the standard deviation of X (math scores).

Inserting our values in gets us: b = 0.824 * (168.9/191.4) = 0.722 (rounded to three decimal places). And a = My - b*Mx = 491.5 - 0.722*504.7 should give us our Y intercept. Plugging in your calculator should give you a roughly around -12.6.

The equation of the regression line would then be Y = -12.6 + 0.722X.

D) To predict the verbal score from a math score of 387, we substitute X = 387 into the regression equation: Y = -12.6 + 0.722 * 387, giving us a predicted verbal score when calculated.

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Answer:

Step-by-step explanation:

false

Yes, All the parabolas have the same domain.

What is Domain?

The set of all inputs of the function is called Domain of set.

Given that;

The statement is,

''All parabolas have the same domain.''

Now,

Since, The domain of the parabola will be (- ∞, ∞).

Hence,  All the parabolas have the same domain.

Thus,  All the parabolas have the same domain.

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Answer:

B is the correct answer.

Step-by-step explanation:

15 times 5 plus 450

= 525

25 times 5 plus 400

= 525

Answer:

[tex]28-2.064\frac{10}{\sqrt{25}}=23.872[/tex]    

[tex]28+2.064\frac{10}{\sqrt{25}}=32.128[/tex]    

So on this case the 95% confidence interval would be given by (23.9;32.1)  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X=28[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=25-1=24[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that [tex]t_{\alpha/2}=2.064[/tex]

Now we have everything in order to replace into formula (1):

[tex]28-2.064\frac{10}{\sqrt{25}}=23.872[/tex]    

[tex]28+2.064\frac{10}{\sqrt{25}}=32.128[/tex]    

So on this case the 95% confidence interval would be given by (23.9;32.1)    

The 95% confidence interval for the average age of the boutique's customers is from 24.1 to 31.9 years, calculated using the sample mean of 28 years, a standard deviation of 10 years, and a sample size of 25.

To calculate a 95% confidence interval for the average age of all customers in the boutique, we will use the sample mean, standard deviation, and the size of the sample along with the z-score corresponding to a 95% confidence level.

The formula for a confidence interval when the population standard deviation is known is:

Confidence interval = {x} (Z  {Σ}/√{n}})

In this case, we have:

Sample mean ({x}): 28 years

Standard deviation (Σ): 10 years

Sample size (n): 25

Z-score for 95% confidence: 1.96 (from z-tables)

First, we calculate the margin of error:

The margin of error = Z{Σ}/{√{n}} = 1.96  {10}/{√{25}} = 1.96 × 2 = 3.92

Then, the confidence interval is:

Lower limit = {x} - Margin of error = 28 - 3.92 = 24.08

Upper limit = {x} + Margin of error = 28 + 3.92 = 31.92

Therefore, the 95% confidence interval for the average age of the boutique's customers is from 24.1 to 31.9 years.

Answer:

The probability that Susan's average score for the week is between 220 and 228 is 0.7594.

Step-by-step explanation:

Average score of Susan = u = 225

Standard deviation = [tex]\sigma[/tex] = 13

Score of Susan follow a Normal Distribution and we have the population standard deviation, as this standard deviation is of her scores of previous 14 years.

In a given week, Susan bowls 16 games. This means, our sample size is 16. So,

n = 16

We have to find the probability that her average score of the week is between 220 and 228. Since the distribution is normal and value of population standard deviation is known, we will use the concept of z-score and z-distribution to find the desired probability.

First we will convert the given numbers to their equivalent z-scores. The formula to calculate the z-scores is:

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

x = 220 converted to z-score will be:

[tex]z=\frac{220-225}{\frac{13}{\sqrt{16}}}=-1.54[/tex]

x = 228 converted to z-score will be:

[tex]z=\frac{228-225}{\frac{13}{\sqrt{16}}}=0.92[/tex]

So, probability that Susan's score is between 220 and 228 is equivalent to probability of z score being in between - 1.54 and 0.92

i.e.

P (220 < X < 228) = P( -1.54 < z < 0.92)

From the z-table we can find the following values:

P( -1.54 < z < 0.92) = P(x < 0.92) - P(x<-1.54)

P( -1.54 < z < 0.92) = 0.8212 - 0.0618

P( -1.54 < z < 0.92) = 0.7594

Since, P (220 < X < 228) is equivalent to P( -1.54 < z < 0.92), we can conclude that the probability that Susan's average score for the week is between 220 and 228 is 0.7594.

Using the Central Limit Theorem and Z-scores, we calculate the probability that Susan's average weekly score will be between 220 and 228 from the standard normal distribution table.

This question revolves around the concept of standard deviation and probability in a normal distribution. Standard deviation measures the dispersion or variation of a set of values. In this case, her average score per week is a random variable, so Central Limit Theorem (CLT) applies because she plays a large number of games (16) every week. CLT states that the sum of a large number of independent and identically-distributed random variables has an approximately normal distribution.

We can calculate the mean (μ) and standard deviation (σ) of the weekly average:

To calculate the Z-scores for 220 and 228:

Finally, we need to find the probability P(Z₁ < Z < Z₂), which involves looking up these Z-scores in a Z-table or using statistical software or online resource that gives the values for a normal distribution.

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Answer:3 foot

Step-by-step explanation:

Answer:

Yes, there is  enough evidence to support the claim that ionizing radiation is beneficial in terms of marketability.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that ionizing radiation is beneficial in terms of marketability.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]

Being π1: the true proportion of treated bulbs that can be comercialized after 240 days, and π2: the true proportion of untreated bulbs that can be comercialized after 240 days.

The significance level is 0.05.

The sample 1, of size n1=180 has a proportion of p1=0.85.

[tex]p_1=X_1/n_1=153/180=0.85[/tex]

The sample 2, of size n2=180 has a proportion of p2=0.65.

[tex]p_2=X_2/n_2=117/180=0.65[/tex]

The difference between proportions is (p1-p2)=0.2.

[tex]p_d=p_1-p_2=0.85-0.65=0.2[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{153+117}{180+180}=\dfrac{270}{360}=0.75[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.75*0.25}{180}+\dfrac{0.75*0.25}{180}}\\\\\\s_{M_d}=\sqrt{0.001+0.001}=\sqrt{0.002}=0.0456[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.2-0}{0.0456}=\dfrac{0.2}{0.0456}=4.382[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=P(t>4.382)=0.000008[/tex]

As the P-value (0.000008) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that ionizing radiation is beneficial in terms of marketability.

Final answer:

The observed marketable rate of irradiated garlic bulbs suggests that ionizing radiation is beneficial to their marketability compared to untreated bulbs, and this could be statistically tested for significance.

Explanation:

The student's data indicates that irradiated garlic bulbs have a significantly higher rate of remaining marketable (85%) after 240 days compared to unirradiated bulbs (65%). Using a significance level of α = 0.05, we can infer a positive effect of ionizing radiation on the marketability of garlic bulbs. To statistically confirm this observation, one could perform a hypothesis test (such as a chi-squared test for independence) to determine if the difference in marketability between the treated and untreated groups is significant.

The sample points in the event A ∪ B are 1, 2, 3, 4, 5, 6, 8, and 10, which is determined by the union.

To identify the sample points in event A ∪ B (the union of events A and B), we need to determine the numbers that satisfy either event A or event B or both.

Event A: The number is even.

Sample points in event A are: {2, 4, 6, 8, 10}.

Event B: The number is less than 7.

Sample points in event B are: {1, 2, 3, 4, 5, 6}.

To find the sample points in the union of events A and B (A ∪ B), we combine the sample points from both events without duplication.

Thus, the sample points in A ∪ B are: {1, 2, 3, 4, 5, 6, 8, 10}.

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The sample points in the event A ∪ B, which include numbers that are either even or less than 7, are {1, 2, 3, 4, 5, 6, 8, 10}.

To find the sample points in the event A ∪ B, where event A: {The number is even} and event B: {The number is less than 7}, we first identify the numbers between 1 and 10 that satisfy each event. For event A, the even numbers between 1 and 10 are 2, 4, 6, 8, and 10. For event B, the numbers less than 7 are 1, 2, 3, 4, 5, and 6.

The union of two events, A ∪ B, includes all sample points that are in event A, event B, or in both A and B. Therefore, the union of A ∪ B includes the even numbers (2, 4, 6, 8, 10) and the numbers less than 7 (1, 2, 3, 4, 5, 6), without listing any number more than once.

Thus, the sample points in the event A ∪ B are {1, 2, 3, 4, 5, 6, 8, 10}.

The question relates to a two-sample t-test in statistics, which compares the means of two processes. It involves calculating a t-score using sample data, and comparing this score to a critical value to determine if there is a significant difference between the two processes.

This question pertains to the field of statistics within mathematics. Specifically, it involves the use of a two-sample t-test to compare the means of two different processes. The two-sample t-test is used when the population standard deviations are unknown but assumed to be equal, which is the case here.

The process involves computing a t-score using the observed data (including sample mean, standard deviation, and sample size) and then comparing this score to a critical value from the t-distribution. If the observed t-score exceeds the critical value, there is evidence to suggest that there is a significant difference between the two processes.

In this case, you would calculate the t-score for Processes A and B using their respective sample means, standard deviations, and sample sizes. If the observed t-score is greater than the critical t-value at the chosen significance level (typically 0.05 or 0.01), we reject the null hypothesis that there is no difference between the two processes.

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Answer: the null hypothesis states that there is no difference between the number of cavities of children who had used either Toothpaste brand X or Toothpaste brand Y for a year.

Step-by-step explanation:

The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.

Looking at the given situation,

The difference was significant at the .05 level. This means that there was enough evidence to reject null hypothesis. Since the null hypothesis contradicts the alternative hypothesis, then the null hypothesis would state that there is no difference between the number of cavities of children who had used either Toothpaste brand X or Toothpaste brand Y for a year.

Answer:

402.12 meters

Step-by-step explanation:

to measure the circumference,

C = 2πr

2π(64) =

to run 1 full lap around the track would be 402.12 meters

i hope this helps!

:)

To find the distance of a full lap around a circular track, calculate the circumference using the formula C = 2π r. With a radius of 64 meters, the distance is approximately 402.12 meters.

To calculate the distance traveled on a full lap around a circular track, you need to find the circumference of the circle. The circumference of a circle is given by the formula C = 2π r, where π (Pi) is approximately 3.14159 and r is the radius of the circle.

Given that the radius of the track is 64 meters, we can substitute this value into the formula to find the circumference.

C = 2π(64 meters)

C = 128π meters

C = approx. 128 × 3.14159 meters

C = approx. 402.1232 meters

Therefore, if you ran one full lap around the circular track, you would travel approximately 402.12 meters.

Answer:

30 hours

Step-by-step explanation:

We can use ratios to solve

5 hours        x hours

-------------- = -------------

3 walls          18 walls

Using cross products

5*18 = 3x

Divide each side by 3

5*18/3 = 3x/3

30 =x

Answer:It will take Harold 30 hours to paint all 18 of the walls

Step-by-step explanation:Your multiplying the amount of walls he is painting by 6 so you do the same to the amount of hours he is painting

Answer:

  x = 1

Step-by-step explanation:

As you might guess, the zeros are symmetrical about the axis of symmetry. That is, the axis of symmetry is midway between the zeros, so will be their average value:

  x = (-2 +4)/2 = 1

The axis of symmetry is x = 1.

Answer:

350(1.137)^20=4563.28232

Answer: inverse operation

Step-by-step explanation:

here you go

Answer:

Combine the like terms

Step-by-step explanation:

2 + 7 = 2x + 5 - 43

The first step is to combine the like terms

9 = 2x - 38

Answer:

Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.

Step-by-step explanation:

Simple interest formula:

The simple interest formula is given by:

[tex]E = P*r*t[/tex]

In which E are the earnings, P is the principal(the initial amount of money), r is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex].

Compound interest formula:

The compound interest formula is given by:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem:

[tex]P = 500, r = 0.08, t = 10[/tex]

So

Simple interest:

[tex]E = P*r*t = 500*0.08*10 = 400[/tex]

In total:

[tex]T = E + P = 500 + 400 = 900[/tex]

Using simple interest, you would withdraw an amount of $900.

Compound interest

We use n = 1

[tex]A = P(1 + \frac{r}{n})^{nt} = 500(1 + \frac{0.08}{1})^{10} = 1079.46[/tex]

You would withdraw $1079.86. Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.

Hey there!

All you have to COMBINE YOUR LIKE TERMS and you have your answer!

-2/3p + 1/5 - 1 + 5/6p

(-2/3p + 5/6p) + (1/5 - 1)

-2/3p + 5/6p = 1/6p

1/5 - 1 = -4/5

Answer: 1/6p + (- 4/5) ✅

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

x = log∨2 (17)

Explanation:

Calculate the difference

Move the constant to the right

Add the numbers

Then take the logarithm of both sides of the equation

Answer:

5

Step-by-step explanation:

The toy rocket will take 2.5 seconds to reach its maximum height, which is 108 feet above the ground.

The question asks about the time it takes for a toy rocket to reach its maximum height and what that maximum height is, given the equation of its height h(t) = -16t2 + 80t + 8. This is a quadratic equation representing the height of the toy rocket as a function of time, which is a typical problem in physics or mathematics dealing with projectile motion. To solve for the time when the rocket reaches its maximum height, we need to find the vertex of the parabola shaped by the quadratic equation where the coefficient of t2 is negative indicating that the parabola opens downwards.

The formula to calculate the time to reach maximum height in a quadratic equation like this is t = -b/(2a), where a is the coefficient of t2 (-16) and b is the coefficient of t (80). Thus, t = -80/(2*(-16)) = 2.5 seconds. To find the maximum height, we plug this time into the height equation: h(2.5) = -16*(2.5)2 + 80*(2.5) + 8 = 108 feet.

Answer:

39% of 118.9=46.371

Step-by-step explanation:

Final answer:

To find out what 39% of a certain amount is equal to 118.9, we can set up an equation and solve for x. To solve "39% of what is 118.9?", we use the equation 0.39x = 118.9 and find that x, which represents the original number, is equal to 305.

Explanation:

To find 39% of a certain number that equals 118.9, we set up the equation where 0.39 (which is 39% as a decimal) times the unknown number (let's call it x) equals 118.9:

0.39x = 118.9

To find the value of x, we divide both sides of the equation by 0.39:

x = 118.9 / 0.39

x = 305

Therefore, 39% of 305 is equal to 118.9.

Answer:

The value of the test statistic is [tex]t = -2.09[/tex]

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 6.6[/tex]

The alternate hypotesis is:

[tex]H_{1} \neq 6.6[/tex]

Our test statistic is:

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

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

In this problem, we have that:

[tex]X = 6.5, \mu = 6.6, \sigma = \sqrt{0.64} = 0.8, n = 280[/tex]

So

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

[tex]t = \frac{6.5 - 6.6}{\frac{0.8}{\sqrt{280}}}[/tex]

[tex]t = -2.09[/tex]

The value of the test statistic is [tex]t = -2.09[/tex]

Answer:

Estimate of the population proportion [tex]\mathbf{\widehat{(P)}}[/tex] = 0.147

Step-by-step explanation:

Given -

Wiley Publications has determined that out of a sample of 7,831 of its publications for 2012, 1,157 of them had been pirated online in some form.

Let x be the no of publication had been pirated online in some form.

x = 1157

n = 7831

Population proportion [tex]\boldsymbol{\widehat{P} = \frac{x}{n}}[/tex]

                                           =  [tex]\frac{1157}{7831}[/tex]

                                         =  0.147