The table value of 95% confidence interval is 1.96

i.e., Z=1.96

Hope this will help you

i.e., Z=1.96

Hope this will help you

Question

asked 2021-05-05

A random sample of \( n_1 = 14 \) winter days in Denver gave a sample mean pollution index \( x_1 = 43 \).

Previous studies show that \( \sigma_1 = 19 \).

For Englewood (a suburb of Denver), a random sample of \( n_2 = 12 \) winter days gave a sample mean pollution index of \( x_2 = 37 \).

Previous studies show that \( \sigma_2 = 13 \).

Assume the pollution index is normally distributed in both Englewood and Denver.

(a) State the null and alternate hypotheses.

\( H_0:\mu_1=\mu_2.\mu_1>\mu_2 \)

\( H_0:\mu_1<\mu_2.\mu_1=\mu_2 \)

\( H_0:\mu_1=\mu_2.\mu_1<\mu_2 \)

\( H_0:\mu_1=\mu_2.\mu_1\neq\mu_2 \)

(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.

(Test the difference \( \mu_1 - \mu_2 \). Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)

(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?

At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are statistically significant.

At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are not statistically significant.

(f) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for

\( \mu_1 - \mu_2 \).

(Round your answers to two decimal places.)

lower limit

upper limit

(h) Explain the meaning of the confidence interval in the context of the problem.

Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.

Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.

Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.

Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

asked 2021-05-09

The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus

\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)

where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.

Part A:

Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.

Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.

Part B:

A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).

Assume the following:

The top speed is limited by air drag.

The magnitude of the force of air drag at these speeds is proportional to the square of the speed.

By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?

Express the percent increase in top speed numerically to two significant figures.

\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)

where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.

Part A:

Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.

Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.

Part B:

A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).

Assume the following:

The top speed is limited by air drag.

The magnitude of the force of air drag at these speeds is proportional to the square of the speed.

By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?

Express the percent increase in top speed numerically to two significant figures.

asked 2021-05-05

The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with \(\displaystyle\mu={1.5}\) and \(\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}\).

(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.

(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).

(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.

(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?

(e) What is the moment generating function for X?

(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.

(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).

(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.

(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?

(e) What is the moment generating function for X?

asked 2021-03-06

asked 2021-02-19

A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?

A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?

A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?

A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?

What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?

A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?

A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).

A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?

A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?

A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?

What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?

A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?

A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).

asked 2021-02-21

How do you solve this problem? I don' t even know whereto begin.

A Ferrari with a mass of 1400 kg approaches a freeway underpassthat is 10 m across. At what speed must the car be moving, inorder for it to have a wavelength such that it might somehow"diffract" after passing through this "single slit"? How dothese conditions compare to normal freeway speeds of 30m/s?

A Ferrari with a mass of 1400 kg approaches a freeway underpassthat is 10 m across. At what speed must the car be moving, inorder for it to have a wavelength such that it might somehow"diffract" after passing through this "single slit"? How dothese conditions compare to normal freeway speeds of 30m/s?

asked 2021-05-23

Random variables \(X_{1},X_{2},...,X_{n}\) are independent and identically distributed. 0 is a parameter of their distribution.

If \(q(X,0)\sim N(0,1)\) is a pivotal function for 0, explain how you would use this result to obtain a symmetrical 95% confidence interval for 0.

If \(q(X,0)\sim N(0,1)\) is a pivotal function for 0, explain how you would use this result to obtain a symmetrical 95% confidence interval for 0.

asked 2020-10-23

1. Find each of the requested values for a population with a mean of \(? = 40\), and a
standard deviation of \(? = 8\)
A. What is the z-score corresponding to \(X = 52?\)
B. What is the X value corresponding to \(z = - 0.50?\)
C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores?
D. What is the z-score corresponding to a sample mean of \(M=42\) for a sample of \(n = 4\) scores?
E. What is the z-scores corresponding to a sample mean of \(M= 42\) for a sample of \(n = 6\) scores?
2. True or false:
a. All normal distributions are symmetrical
b. All normal distributions have a mean of 1.0
c. All normal distributions have a standard deviation of 1.0
d. The total area under the curve of all normal distributions is equal to 1
3. Interpret the location, direction, and distance (near or far) of the following zscores: \(a. -2.00 b. 1.25 c. 3.50 d. -0.34\)
4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with \(\mu = 78\) and \(\sigma = 12\). Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: \(82, 74, 62, 68, 79, 94, 90, 81, 80\).
5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about \($12 (\mu = 42, \sigma = 12)\). You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is $44.50 from tips. Test for a difference between this value and the population mean at the \(\alpha = 0.05\) level of significance.

asked 2021-02-19

An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a constant torque of \(\displaystyle{1950}\ {N}\cdot{m}\) to the propeller, which starts from rest.

a) What is the angular acceleration of the propeller? Model the propeller as a slender rod.

b) What is the propeller's angular speed after making 5.00 revolutions?

c) How much work is done by the engine during the first 5.00 revolutions?

e) What is the instantaneous power output of the motor at the instant that the propeller has turne through 5.00 revolutions?

a) What is the angular acceleration of the propeller? Model the propeller as a slender rod.

b) What is the propeller's angular speed after making 5.00 revolutions?

c) How much work is done by the engine during the first 5.00 revolutions?

e) What is the instantaneous power output of the motor at the instant that the propeller has turne through 5.00 revolutions?

asked 2021-03-15

Three long wires (wire 1, wire 2,and wire 3) are coplanar and hang vertically. The distance betweenwire 1 and wire 2 is 16.0 cm. On theleft, wire 1 carries an upward current of 1.50 A. To the right,wire 2 carries a downward current of 3.40 A. Wire 3 is located such that when itcarries a certain current, no net force acts upon any of the wires.

(a) Find the position of wire 3, relative to wire 1.

(b) Find the magnitude and direction of the current in wire 3.

(a) Find the position of wire 3, relative to wire 1.

(b) Find the magnitude and direction of the current in wire 3.