A beam of light shines on an equilateral glass prism at an angle of 45∘ to one face (figure (a) below). 1) What is the angle at which the light emerges from the opposite face given that nglass = 1.57? (Express your answer to three significant figures.)

2) Now consider what happens when dispersion is involved (figure (b)). Assume the incident ray of light spans the spectrum of visible light between 400 nm and 700 nm (violet to red, respectively). The index of refraction for violet light in the glass prism is 1.572, and it is 1.568 for red light in the glass prism. Find the distance along the right face of the prism between the points where the red light and violet light emerge back into air. Assume the prism is 10.0 cm on a side and the incident ray hits the midpoint of the left face. (Express your answer to two significant figures.)

QUESTION 3 [20 MARKS]

a. State any five (5) factors that often restrict the sample size.

b. Explain with reasons the most suitable measurement scale that a researcher can use from these sampled statements: i. Female soccer teams in this year’s Olympics. ii. Number of countries in Africa. iii. Seasons in a year.

c. Distinguish Secondary literature from Primary literature use examples to justify your answer.

PART A) The color of tulips can be determined by the interaction of 2 loci. Tulips can be pigmented red (controlled by a dominant allele, R) or yellow (r). The second locus has a dominant white allele (W), which inhibits pigment resulting in white tulips and a recessive allele (w) which results in colored petals. Consider the cross of a true breeding yellow tulip with a true breeding white tulip that is heterozygous recessive at the pigmented locus. Show work where necessary. What are the parental genotypes? What are the resulting F1 genotypes? If you cross the F1 plants what is the probability of getting a white tulip in the F2 generation?

PART B) A true-breeding pink-body unicorn with a red horn was crossed with a true-breeding white-bodied, purple horned unicorn. Pink body and purple horns are dominant. What phenotypic ratio do you expect for F1? For the F2 generation, you end up with the following unicorn offspring: 180 pink-bodied and purple horned, 60 pink-bodied and red horned, 50 white-bodied and purple horned, and 15 white bodied and red horned. Test the hypothesis that the genes associated with unicorn body and horn color are assorting independently. What is your chi-square value?  Now assume that your chi-square value exceeds the chi-square critical value. Does this mean you reject or fail to reject your null hypothesis.  Now assume that you failed to reject your null hypothesis, does this mean the two genes are independently assorting or that linkage is occurring?

1. In your business, describe a decision you would need to make where you would want to use some type of optimization tool. In regards to this decision, explain the importance of optimizing and how it will be beneficial for your business.

2. Think of an example where simulation could be beneficial to your business. Explain how you could use simulation and describe the type of simulation. (There are several listed in the text. i.e. probabilistic, time-dependent/independent, discrete event, visual, etc…) Be as specific as possible in your description, including possible advantages and disadvantages of using the simulation you described.

P. S - We are talking about the company called Urban Clap. A simple google search will you about the company.

Need both the answers one one paragraph each and please computer typing.. Will rate your answer for sure. Thanks

One Way ANOVA

The “Award” variable represents whether the student said that they would prefer to win an Academy Award, Nobel Prize, or Olympic Medal. The “SAT” variable is the students’ total SAT score (Verbal + Math). We want to compare the SAT scores for the three Award categories. Remember to include all relevant output that supports your answers. And, remember to clearly identify your final answer from any output used.

A. Use Minitab Express to compute the mean and standard deviation of total SAT scores for students who selected each of the three different awards. Include your output below.

B. Use Minitab Express to construct side-by-side boxplots to compare the total SAT scores for students who selected each of the three different awards. Copy + paste your graph here.

C. Based on the boxplot created in part b, do you think the average SAT score statistically differs by award? Explain.

D. Use Minitab Express to conduct a one-way ANOVA to compare the mean total SAT scores for students who selected each of the three different awards. Use the five-step hypothesis testing procedure.

Step 1: State hypotheses and check assumptions

Step 2: Compute the test statistic

Step 3: Determine the p-value

Step 4: Make a decision (reject or fail to reject the null)

Step 5: State a real world conclusion

E. Use Minitab Express to conduct Tukey simultaneous tests for differences in means. Remember to include your relevant output here. Clearly state which pairs are different and which pairs are not different.

F. Explain why it would not be appropriate to just conduct a series of three independent means t tests in this scenario.

REQUIRED FILE:

https://www.upload.ee/files/8711961/StudentSurvey.MTW.html

Question 13.5 pts

Using the following data coming from the population find mean.

1, 1, 1, 11, -9

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Question 23.5 pts

Using the following data coming from the population find variance.

1, 1, 1, 11, -9

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Question 33.5 pts

Using the following data coming from the sample find variance.

1, 1, 1, 11, -9

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Question 43.5 pts

Using the following data coming from the population find standard deviation.

1, 1, 1, 11, -9

Round your answer to the nearest hundredths.

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Question 53.5 pts

Using the following data coming from the population find its mode.

3, 3 ,7,-2, 0, 1

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Question 63.5 pts

Using the following data coming from the population find its median..

3, 3 ,7,-2, 0, 1

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Question 73.6 pts

What is the sample space of the following experiment?

You are tossing a coin 4 times and recording if total number of heads (in all tosses) is even or odd.

Give your answer using set notation, i.e. list all elements of the sample space in braces {} and separate them with a comma. Do not include spaces.

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Question 83.6 pts

How many elements are in the following sample space?

You are rolling a die 2 times and recording the sum of two numbers you rolled.

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Question 93.5 pts

What is the sample space of the following experiment?

You are selecting a ball from a jar with 4 red, 5 blue, and 6 green balls. You record its color.

Give your answer using set notation, i.e. list all elements of the sample space in braces {} and separate them with a comma. Do not include spaces.

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Question 103.6 pts

. Based on the following tabled answer the question below.

We select randomly one person from the group. Find the probability that it is a child. Write your answer as a decimal.

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Question 113.6 pts

Based on the following tabled answer the question below.

We select randomly one person from the group. Find the probability that it is a child OR a female. Write your answer as a decimal.

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Question 123.6 pts

Based on the following tabled answer the question below.

We select randomly one person from the group. Find the probability that it is a child AND a female. Write your answer as a decimal.

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Question 133.6 pts

ased on the following tabled answer the question below.

We select randomly one person from the group. Find the probability that it is a child given that it is a male. Write your answer as a decimal.

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Question 143.6 pts

A card is drawn from a standard deck of 52 cards and the result is recorded.What is the probability that a king is drawn?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 153.6 pts

A card is drawn from a standard deck of 52 cards and the result is recorded.What is the probability that a king OR black card is drawn?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 163.6 pts

A card is drawn from a standard deck of 52 cards and the result is recorded.What is the probability that a king is drawn given that we know that a red card was drawn?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 173.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer. Two shirts are selected in a row with replacement. What is the probability that both are red?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 183.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer. Two shirts are selected in a row without replacement. What is the probability that both are red?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 193.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer. One shirt is selected and returned to the drawer and then the second shirt is selected. What is the probability that one is blue and one is green?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 203.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer. Two shirts are selected in a row without the replacement. What is the probability that the second one is red given that the first one blue?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 213.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer.A shirt is selected and returned to the drawer and then the second shirt is selected. What is the probability that both are of the same color?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 223.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer. A shirt is selected and returned to the drawer and then the second shirt is selected. What is the probability that the second one is red given that the first one blue?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 233.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer. A shirt is selected and returned to the drawer and then the second shirt is selected. What is the probability that at least one green shirt will be selected?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 243.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer. A shirt is selected and then, without replacement, the second shirt is selected. What is the probability that at least one red shirt will be selected?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 253.6 pts

There are 10 red, 5 blue and 3 green shirts in a drawer. A shirt is selected and returned to the drawer and then the second shirt is selected. What is the probability that the shirts are of different color?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

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Question 263.6 pts

A committee of eight people must choose a president, a vice president, and a secretary. In how many ways can this be done?

Draw a supply and a demand curve and label the market equilibrium on the axes with P1 and Q1.

Illustrate the effect of an increase in demand on price and quantity. Label the new equilibrium values on the axes with P2 and Q2.

In your own words and in detail explain the market adjustment leading to the new equilibrium.
Show the relevant elements of your explanation in the graph

1. Objective: To determine how well a categorical sample distribution fits into a claimed population distribution.

All plain M&Ms in the U.S. are manufactured at two different factories—one in New Jersey, and one in Tennessee. The factories produce different color distributions, as shown below.

Professor Gomez buys a 3.14oz bag of M&M’s. Of the 112 M&M’s in the bag, there were 30 blue, 26 orange, 25 green, 9 yellow, 18 red, and 4 brown.

(a) Fill out the tables below with the expected values at each factory.

(b) Use expected values from the New Jersey factory to perform a goodness-of-fit test with α = 0.01.

Check the assumptions:

Calculate the test statistic  =  by completing the following table:

Critical Value =  =

Decision:

(c) Use the expected values from the Tennessee factory to perform a goodness-of-fit test with α = 0.01.

Check the assumptions:

Use the GOF-Test on your graphing calculator to find the test statistic.  ____________

Critical Value =  =

Decision:

(d) According to the goodness-of-fit tests, where was this bag of M&Ms likely manufactured

Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below:

First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=84,n2=88,x1=43x2=38

Is there evidence, at an ?=0.08 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (??,a) is expressed (-infty, a), an answer of the form (b,?) is expressed (b, infty), and an answer of the form (??,a)?(b,?) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Do Not Reject H0.
B. Reject H1.
C. Reject H0.
D. Do Not Reject H1.

2) 1. In a study of red/green color blindness,

550 men and 2150 women are randomly selected and tested. Among the men, 50have red/green color blindness. Among the women, 4 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.
The test statistic is  
The p-value is  
Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women using the 0.05% significance level?

A. No
B. Yes

2. Construct the 95% confidence interval for the difference between the color blindness rates of men and women.
<(p1?p2)<  

Which of the following is the correct interpretation for your answer in part 2?
A. There is a 95% chance that that the difference between the rates of red/green color blindness for men and women lies in the interval
B. We can be 95% confident that the difference between the rates of red/green color blindness for men and women lies in the interval
C. We can be 95% confident that that the difference between the rates of red/green color blindness for men and women in the sample lies in the interval
D. None of the above