A researcher wants to conduct a before/after study on 12 subjects to determine if a treatment results in any difference in scores. Scores are obtained on the subjects both before and after the treatment. After subtracting the after scores from the before scores, the average difference is computed to be 3.40 with a sample standard deviation of 1.21. Assume that the differences are normally distributed in the population. If the researcher wanted to construct a 98% confidence interval for the difference between the (after - before) means, the t value to be used in the computations will be

A) 2.3027

B) 2.3281

C) 2.6810

D) 2.7181

A recent study reported that 51​% of the children in a particular community were overweight or obese. Suppose a random sample of 500 public school children is taken from this community. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of​ overweight/obese children in the sample will be greater than 0.47. Complete parts​ (a) and​ (b) below. . Calculate the probability that 47​% or more of the sample are overweight or obese.

A statistician calculates that 7% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 613 Americans would differ from the population proportion by greater than 3% ? Round your answer to four decimal places.

A mathematics achievement test is given to students prior to entering a certain college. A sample of 10 students was selected and their progress in calculus observed:

e) Complete the ANOVA table for the least squares estimate for the regression line.

f)  Test at the 5% significance level whether the model is useful for predicting the final calculus grade.

g)  Give a 95% confidence interval for the mean final calculus grade when the achievement test score is 50.

h) Give a 95% prediction interval for the final calculus grade when the achievement test score is 50. Is the interval wider or narrower than the confidence interval? Why?

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 89 words per minute​ (wpm) and a standard deviation of 10 wpm. A teacher instituted a new reading program at school.

After 10 weeks in the​ program, it was found that the mean reading speed of a random sample of 22 second grade students was 91.2 wpm. What might you conclude based on this​ result?

Select the correct choice below and fill in the answer boxes within your choice. ​(Type integers or decimals rounded to four decimal places as​ needed.)

A. A mean reading rate of 91.2 wpm is not unusual since the probability of obtaining a result of 91.2 wpm or more is ____. This means that we would expect a mean reading rate of 91.2 or higher from a population whose mean reading rate is 89 in _____ of every 100 random samples of size n=22 students. The new program is not abundantly more effective than the old program.

B. A mean reading rate of 91.2 wpm is unusual since the probability of obtaining a result of 91.2 wpm or more is ______. This means that we would expect a mean reading rate of 91.2 or higher from a population whose mean reading rate is 89 in _____ of every 100 random samples of size n=22 students. The new program is abundantly more effective than the old program.

Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. Five percent of workers in a city use public transportation to get to work. You randomly select 254 workers and ask them if they use public transportation to get to work. Complete parts (a) through (d).

Can the normal distribution be used to approximate the binomial distribution?

A.

Yes, because both

np greater than or equals≥5

and

nq greater than or equals≥5.

B.

No, because

nq less than<5.

C.

No, because

np less than<5.

(a) Find the probability that exactly

1919

workers will say yes.

What is the indicated probability?

nothing

(Round to four decimal places as needed.)

Sketch the graph of the normal distribution with the indicated probability shaded.

(b) Find the probability that at least

77

workers will say yes.

What is the indicated probability?

nothing

(Round to four decimal places as needed.)

Sketch the graph of the normal distribution with the indicated probability shaded.

A.

1317x

mu equals 12.7μ=12.7

x y graph

B.

1317x

mu equals 12.7μ=12.7

x y graph

C.

1317x

mu equals 12.7μ=12.7

x y graph

D.

The normal distribution cannot be used to approximate the binomial distribution.

(c) Find the probability that fewer than

1919

workers will say yes.

What is the indicated probability?

nothing

(Round to four decimal places as needed.)

Sketch the graph of the normal distribution with the indicated probability shaded.

A.

13119x

mu equals 12.7μ=12.7

x y graph

B.

13119x

mu equals 12.7μ=12.7

x y graph

C.

13119x

mu equals 12.7μ=12.7

x y graph

D.

The normal distribution cannot be used to approximate the binomial distribution.

(d) A transit authority offers discount rates to companies that have at least

3030

employees who use public transportation to get to work. There are

499499

employees in a company. What is the probability that the company will not get the discount?

Can the normal distribution be used to approximate the binomial distribution?

A.

No, because

npless than<5.

B.

Yes, because both

npgreater than or equals≥5

and

nqgreater than or equals≥5.

C.

No, because

nqless than<5.

What is the probability that the company will not get the discount?

nothing

(Round to four decimal places as needed.)

Sketch the graph of the normal distribution with the indicated probability shaded.

Finally, you decide to repeat this same procedure to examine salaries among male accountants in your firm. You do not necessarily expect salaries to be larger or smaller than the average. The same large national survey of male accounts found that the average salary was $60,000 with a SD of $5,500. After sampling 55 male accountants in your organization, you find their average salary is $57,000. Use a two-tailed z-test at the 5% level of significance to determine if there is a significant difference between the male national average and male salaries in your company. 9. State alternative hypothesis 10. State null hypothesis 11. List your test statistic 12. Is this difference statistically significant?

M/PF Research, Inc. lists the average monthly apartment rent in some of the most expensive apartment rental locations in the United States. According to their report, the average cost of renting an apartment in Minneapolis is $951. Suppose that the standard deviation of the cost of renting an apartment in Minneapolis is $96 and that apartment rents in Minneapolis are normally distributed. If a Minneapolis apartment is randomly selected, what is the probability that the price is: (Round the values of z to 2 decimal places. Round answers to 4 decimal places.) (a) $980 or more? (b) Between $930 and $1,110? (c) Between $840 and $930? (d) Less than $720?

The epicenter of an earthquake is the point on Earth's surface directly above the earthquakes origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Find the location of the earthquake's epicenter if it is 3 miles away from A(2,3), 4 miles away from B(-5,3), and 5 miles away from C(-1,-2).

Perpbisogram Definition: A perpbisogram of a quadrilateral is a polygon formed by the perpendicular bisectors of the sides of the quadrilateral.

Prove the following theorem

1. The angles of a trapezoid are congruent to the angles of its perpbisogram.

(SHOW DIAGRAM)

Given Δ ABC , construct equilateral triangles Δ BCD , Δ CAE , and Δ ABF outside of Δ ABC . Prove that the circumcircles of Δ BCD , Δ CAE , and Δ ABF are concurrent (go through the same point).

Assume that G is connected and let
                   (G) = min{deg(v) ∈ Z ≥0 | v ∈ V (G)}
denote the lowest vertex degree that occurs in a graph G and let
                    λ(G) = min{|K| ∈ Z ≥0 | K ⊆ E(G) is a cutset of G}
denote the edge connectivity of G.
Prove that λ(G) ≤ δ(G)

Prove both of the following theorems in the context of Incidence Geometry. Your proofs should be comparable in terms of rigor and precision (and clarity of thought!) to the ones done in class today.

A1. Given any point, there is at least one line not passing through it,

A2. Given any point, there are at least two lines that do pass through it,

The first cake has three layers with each one having a different top view: the bottom is a square, the middle is a hexagon, and the top is a circle. The height of each layer may vary. The second cake has three layers with a top view of concentric circles. All three layers have the same height. The diameter of the middle layer is 20% larger than the top layer, and the diameter of the bottom layer is 25% larger than the middle layer.

Your data given is:

length of the side of cake1 square layer = 20

height of cake1 square layer = 1

length of the side of cake1 hexagon layer = 9

height of cake1 hexagon layer = 10

  diameter of cake1 circular layer =5

height of cake1 circular layer = 7

diameter of cake2 bottom layer = 68

The ratio of the volume of each layer to the volume of cake1 is 0.1514(square), 0.7966(hexagon), 0.052(cylinder)

Find:

1) The height of cake2

2) The total surface area of cake2

3) The volume of cake2

Answers should be: (I just don't know how toget there)

Second cake:
* total height: 1.047
* surface area: 3815.5796
* volume: 2641.8863