# An article in Chance magazine reported on the Houston Independent School District's magnet schools programs. Of the 1755 qualified applicants, 931 were accepted, 300 were wait-listed, and 524 were turned away for lack of space. Find the relative freuqency distribution of the decisions made and write a sentence describing it.

Question
Describing quantitative data
An article in Chance magazine reported on the Houston Independent School District's magnet schools programs. Of the 1755 qualified applicants, 931 were accepted, 300 were wait-listed, and 524 were turned away for lack of space. Find the relative freuqency distribution of the decisions made and write a sentence describing it.

2021-02-26
Given:
1755 qualifed applicants in total
931 accepted
300 wait-listed
524 turned away for lack of space
The relative frequency if obtainded by dividing the frequency by its total frequency.
Accepted: $$\displaystyle\frac{{931}}{{1755}}\sim{0.5305}={53.05}\%$$
Wait-listed: $$\displaystyle\frac{{300}}{{1755}}=\frac{{20}}{{117}}\sim{0.1709}={17.09}\%$$
Turned away: $$\displaystyle\frac{{512}}{{1755}}\sim{0.2969}={29.69}\%$$
53.05% of the qualifed applicants were accepted, 17.09% were wait-listed and 524 were turned away for lack of space.

### Relevant Questions

An analyst produced the following summary statistics describing a quantitative variable:
n Mean Variance Std. dev. Median Range Q1 Q3
108 79.9 64.63 8.04 79.05 44.7 74 85.4
(a) The smallest value in the data set is 51. Should the analyst consider the value 51 to be an outlier on the low side?
(b) Justify your answer using an appropriate outlier identification rule. If you perform a calculations, give the pertinent calculations. If you create a graph, copy and paste it into the space.
True or False
1.The goal of descriptive statistics is to simplify, summarize, and organize data.
2.A summary value, usually numerical, that describes a sample is called a parameter.
3.A researcher records the average age for a group of 25 preschool children selected to participate in a research study. The average age is an example of a statistic.
4.The median is the most commonly used measure of central tendency.
5.The mode is the best way to measure central tendency for data from a nominal scale of measurement.
6.A distribution of scores and a mean of 55 and a standard deviation of 4. The variance for this distribution is 16.
7.In a distribution with a mean of M = 36 and a standard deviation of SD = 8, a score of 40 would be considered an extreme value.
8.In a distribution with a mean of M = 76 and a standard deviation of SD = 7, a score of 91 would be considered an extreme value.
9.A negative correlation means that as the X values decrease, the Y values also tend to decrease.
10.The goal of a hypothesis test is to demonstrate that the patterns observed in the sample data represent real patterns in the population and are not simply due to chance or sampling error.
Identify the population: An education professor wants to gather information about parental involvement in early education for students attending a particular Ivy League university. She obtains a list of registered students from the registrar's office and randomly chooses 300 students to study.
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
In an exit poll during the 2004 presidential election, voters were asked to name the issue that most affected their vote for a candidate for presidency. The following table summarizes their responses.
Moral Values: 22%
Economy/jobs: 20%
Terrorism: 19%
Iraq: 15%
Health Care: 8%
Taxes: 5%
Education: 4%
As you will notice, these percentages add up to 93%. Assume that the remaining 7% of these voters names other issues and let us denote these issues as Other. Draw a bar graph to display these data.
Consider the following research questions/study scenarios. For each study, discuss the most appropriate methods for describing the data (graphically and numerically). What statistical method would be most appropriate for addressing the research questions? Be sure to provide justification of the statistical method. Provide the appropriate regression model and statistical test when appropriate.
1.A study was performed to determine the differences in pain experienced by children with sickle cell disease (SCD) in inpatient and outpatient settings. Pain intensity (visual analog scale) was the primary outcome of interest, but potential confounders include age and physical activity.
The article “Anodic Fenton Treatment of Treflan MTF” describes a two-factor experiment designed to study the sorption of the herbicide trifluralin. The factors are the initial trifluralin concentration and the $$\displaystyle{F}{e}^{{{2}}}\ :\ {H}_{{{2}}}\ {O}_{{{2}}}$$ delivery ratio. There were three replications for each treatment. The results presented in the following table are consistent with the means and standard deviations reported in the article. $$\displaystyle{b}{e}{g}\in{\left\lbrace{m}{a}{t}{r}{i}{x}\right\rbrace}\text{Initial Concentration (M)}&\text{Delivery Ratio}&\text{Sorption (%)}\ {15}&{1}:{0}&{10.90}\quad{8.47}\quad{12.43}\ {15}&{1}:{1}&{3.33}\quad{2.40}\quad{2.67}\ {15}&{1}:{5}&{0.79}\quad{0.76}\quad{0.84}\ {15}&{1}:{10}&{0.54}\quad{0.69}\quad{0.57}\ {40}&{1}:{0}&{6.84}\quad{7.68}\quad{6.79}\ {40}&{1}:{1}&{1.72}\quad{1.55}\quad{1.82}\ {40}&{1}:{5}&{0.68}\quad{0.83}\quad{0.89}\ {40}&{1}:{10}&{0.58}\quad{1.13}\quad{1.28}\ {100}&{1}:{0}&{6.61}\quad{6.66}\quad{7.43}\ {100}&{1}:{1}&{1.25}\quad{1.46}\quad{1.49}\ {100}&{1}:{5}&{1.17}\quad{1.27}\quad{1.16}\ {100}&{1}:{10}&{0.93}&{0.67}&{0.80}\ {e}{n}{d}{\left\lbrace{m}{a}{t}{r}{i}{x}\right\rbrace}$$ a) Estimate all main effects and interactions. b) Construct an ANOVA table. You may give ranges for the P-values. c) Is the additive model plausible? Provide the value of the test statistic, its null distribution, and the P-value.
A researcher was interested in the effectiveness of a new drug for testosterone replacement in adult men between the ages of 40 and 59 in the U.S. who are experiencing symptoms related to abnormally low testosterone levels. According to the 2010 Census data, there were 36,135,061 men between the ages of 40 and 59 in the U.S. 100 U.S. men participated in a clinical trial of the drug. Those 100 men were classified by race and ethnicity (White, Asian, Black, Hispanic, Native, Islander, Other) and their average testosterone level was 275 $$\displaystyle\frac{{{n}{g}}}{{{d}{L}}}$$. The average testosterone level of all adult men in the U.S. between 40 and 59 is 565 ng/dL. Use this information for problems A-E