Identify a similarity and a difference between two objects – one in static equilibrium and the other in dynamic equilibrium? Hint: think about net force and motion

If we push an object at constant velocity, how much friction acts on the object compared to our pushing force:

A) equal to the pushing force

B) greater than the pushing force

C) less than the pushing force

D) none of the above

By how much does the gravitational force between two objects decrease when the distance between their centers is doubled?

A) ½

B) ¼

C)1/8

D) 1/16

E)1/32

What happens to the acceleration of a cart if the force acting on it is quadrupled (i.e. multiplied by 4)

Tim stands in the middle of a scaffold. There is no motion. The left scale reads 450N. What is the reading on the right scale and the total weight of Tim and scaffold

A) 450N and 900N

B) 450N and 1200N

C) 400N and 850N

D) 250N and 700N

E) 1050N and 1500N

What is the force of gravity on a 2 kg mass 3.2*106 m above the Earth’s surface. The mass of the earth is 6.4*1023 kg and its radius is 6.4*106 m. Hint: the total distance between the object and the earth is from the center of the earth to the location of the object.

If two objects – one three times as heavy as the other – are in free fall, which of these statements are true:

I) The force of gravity on the heavier object is 3 times that on the lighter object

II) Their speeds are increasing at the same rate i.e. they are falling at the same rate

III) The heavier object is falling much faster than the smaller object

A) All of the above

B) none of the above

C) I and II

D) I and III

E) I only

Which of these is not a law of motion?

A) Action and reaction are equal and opposite

B) The acceleration of an object is directly proportional to the net force acting on the object

C) A body at rest or in motion continues in its state of rest or uniform motion unless a force is applied to it

D) The earth always attracts objects to its center

Define terminal velocity? Can it be reached in a vacuum? Why or why not?

What is the difference between the atomic number and the mass number of an element?

Fusion is the source of energy in the sun. What is the difference between fission and fusion?

Which of these is not an element:

A) O2

B) N2

C) He

D) Cl

E) HF

What is the IUPAC name for KCl?

Hydrogen is the lightest (least heavy) element/gas. Why is it not used to fill children’s balloons? Why is helium used?

Why is there more carbon-14 in living bones than in once-living ancient bones of the same mass?

A radon atom emits a beta particle and then is irradiated with gamma rays, what is the final element? Its mass number and atomic number?

How many valence electrons are in these elements:

a) oxygen

b) boron

c) silicon

d) krypton

Which of these are true of gamma rays:

i) Its frequency is lower than ultraviolet radiation

ii) Gamma irradiation can be used to destroy harmful micro-organisms

iii) They are electromagnetic waves

iv) They can bring about genetic mutations in humans

A) i only

B) ii only

C) ii, iii and iv

D) all of the above E) none of the above

Which of these radioactive particles do not penetrate the skin?

A) Alpha particle

B) beta-particle

C) gamma rays

D) none of the above

What happens when an atom loses an electron?

A) it becomes positively charged because there are more protons than neutrons

B) it becomes positively charged because there are more protons than electrons

C)it remains neutral

D) it is a form of radioactive decay

E) none of the above

When alpha particles pick up electrons, they become _________

A) Helium gas

B) Hydrogen gas

C) Lithium

D) remain alpha particles

E) none of the above

For n = 6, from N(μ, σ2) where the variance is only estimated, consider:  = .91. What is the value of q?
• For n = 6, from N(μ, σ2) where the variance is only estimated, consider: = .91. What is the value of q?
• For n = 6, from N(μ, σ2) where the variance is only estimated, consider: . Is this probability less than, greater than, or equal to .92? Explain.
• For n = 6, from N(μ, σ2) where the variance is only estimated, consider: . Is this probability less than, greater than, or equal to .95? Explain.
• Given a sample of size n from N(μ, σ2), what is ?
• Given a sample of size n from N(μ, σ2), what is (approximately)?
• If you were constructing a confidence interval for a collection of 17 data points (where the variance is unknown), what distribution exactly would you use?
• Suppose you have decided to gather some known fixed number n of observations, and create a confidence interval at some given confidence level c, where the variance of the underlying population will be estimated. Before you gather your n numbers, don’t know how big your margin of error will be. Explain why.
• Suppose you have decided to gather some known fixed number n of observations, and create a confidence interval at some given confidence level c, where the variance of the underlying population will be estimated. Before you gather your n numbers, you don’t know how long your confidence interval will be. Explain why.
• Calculate the appropriate ratio to determine how many times larger the length of a confidence interval (at the 96% confidence level) is when the variance is only estimated from a data set with 6 observations (and a mean of 4 and standard deviation of 3), than when the variance is assumed to be known.
• Calculate the appropriate ratio to determine how many times larger the margin of error (at the 96% confidence level) is when the variance is only estimated from a data set with 6 observations (and a mean of 4 and standard deviation of 3), than when the variance is assumed to be known.

For n = 6, from N(μ, σ2) where the variance is only estimated, consider:  = .91. What is the value of q?

• Calculate the appropriate ratio to determine how many times larger the quantile used in a 98% confidence interval is when the variance is only estimated from a data set with 6 observations (and a mean of 4 and standard deviation of 3), than when the variance is assumed to be known.

• Calculate a 95% confidence interval for the data set {3, 5, 2, 1, 3}. Recognize that your estimate of the variance is only an estimate.
• Calculate a 99% confidence interval for a data set of 14 observations, whose mean is 6.2, and whose standard deviation is estimated to be 7.
• Calculate a 99% confidence interval for a data set of 14 observations, whose mean is 6.2, and whose variance is estimated to be 7.
• Using confidence intervals, explain how having a fairly large size of n can help you get a better sense of what the true value of  really is (since your point estimate is unlikely to be exactly correct).

• Does the size of n affect how likely it is that you will obtain a confidence interval that contains ? Explain.
130. If you are using student’s T distribution with 11 degrees of freedom, how large was your sample?

131. When the variance is unknown, what distribution do we refer to when constructing a confidence interval for the mean, when the sample has 18 observations in it?
132. What is the formula for the margin of error when the variance is unknown? Label the parts
133. What is the formula for the upper bound of a confidence interval when the variance is unknown? Label the parts – do not simply specify the margin of error; give that in terms of its parts and label them.
134. What is the formula for the lower bound of a confidence interval when the variance is unknown? Label the parts – do not simply specify the margin of error; give that in terms of its parts and label them.
• “My 95% confidence interval is (20, 30), so there is a 95% chance that the true mean μ is somewhere between 20 and 30.” Explain what is wrong with this claim.
135. A report gives a confidence interval of (223.83, 325.76). What are and the margin of error?
136. A report gives a point estimate of 156.78 with a margin of error of 23.42. What is the corresponding confidence interval?

• When investigating a probability distribution of some population of interest, we frequently explore its parameters by adverting to a different probability distribution. What is this other distribution, and why do we use it?
130. When estimating the mean of a probability distribution of some population of interest (variance known), a confidence interval is typically constructed using a normal distribution, even if the underlying population distribution is not normal. Why is this done?
131. If the length of my confidence interval is 9, what is my margin of error?
132. If my margin of error is 5, what is the length of my confidence interval?

133. If my margin of error is 5, how long is my confidence interval if I double the size of my data (assume all other quantities remain the same)?
134. If my margin of error is 5, what is it if I double the size of my data (assume all other quantities remain the same)?
135. If the length of my confidence interval is 8, how long is it if I double the size of my data (assume all other quantities remain the same)?
136. Construct a margin of error (at the 94% confidence level) for the mean for the data set {3, 2, -2, 0}.
• Suppose q and F are the quantile function and cdf of a given distribution. What is F(q(p))? Explain.

• Suppose q and F are the quantile function and cdf of a given distribution. What is q(F(x))? Explain.
130. Describe the role that the Central Limit Theorem plays in our construction of confidence intervals.
131. If you have two data sets that yield identical estimates of the variance, but for the first one you used 20 observations and for the second you used 30, which one will have the larger margin of error? Calculate/explain/prove your answer.
• Suppose you have decided to gather some fixed number n of observations, and create a confidence interval at some confidence level c, where the variance of the underlying population is known to be 2. Before you even gather your n numbers, you already know how big your margin of error will be. Explain why.
• Suppose you have decided to gather some fixed number n of observations, and create a confidence interval at some confidence level c, where the variance of the underlying population is known to be 2. Before you even gather your n numbers, you already know how long the confidence interval will be. Explain why.
132. In estimating the mean of X (where X has a known standard deviation of 5), your 94% confidence interval had a total length of (approximately) 7. What is the length of the confidence interval if you change the confidence level to 98%?

133. In estimating the mean of X (where X has a known standard deviation of 5), the size of your 94% margin of error was (approximately) 7. What is the size of the margin of error if you change the confidence level to 98%?
134. In estimating the mean of X, your 94% confidence interval had a total length of (approximately) 7. What is the (approximate) size of n if the known standard deviation of X is 3?

Using question 131)
135. In estimating the mean of X, the size of your 94% margin of error was (approximately) 7. What is the (approximate) size of n if the known standard deviation of X is 3?
136. In a given study, how (if at all) would increasing the size of the error probability  affect the length of a confidence interval?

# Justices

Justices of the peace must have proven ability and experience in making sound, practical and timely decisions involving complex factors. Please describe your best example of a time when sought information needed to solve a problem, how the information was analyzed and how you came to a decision. What was the decision? What effect, if any, did your decision have?

# CJA 364 Week 5

Identify and discuss the steps in a jury trial. In the analysis be sure to assess the constitutional trial rights that are enacted during a jury trial, as well as examine and discuss the selection of a fair and unbiased jury.