# 1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation: begin{array}{c} Gender hline Affilation & Male & Female hline Democrat & 300 & 600 Republican & 500 & 300 Other & 200 & 100 hline end{array} What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents: begin{array}{c} Size of Car hline Gender & Small & Medium & lange & Total hline Female & 58 & 63 & 17 & 138 Male & 79 & 61 & 25 & 165 Total & 137 & 124 & 42 & 303 hlin

Question
Modeling data distributions
1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation: $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{G}{e}{n}{d}{e}{r}\backslash{h}{l}\in{e}{A}{f}{f}{i}{l}{a}{t}{i}{o}{n}&{M}{a}\le&{F}{e}{m}{a}\le\backslash{h}{l}\in{e}{D}{e}{m}{o}{c}{r}{a}{t}&{300}&{600}\backslash{R}{e}{p}{u}{b}{l}{i}{c}{a}{n}&{500}&{300}\backslash{O}{t}{h}{e}{r}&{200}&{100}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents: $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{S}{i}{z}{e}\ {o}{f}\ {C}{a}{r}\backslash{h}{l}\in{e}{G}{e}{n}{d}{e}{r}&{S}{m}{a}{l}{l}&{M}{e}{d}{i}{u}{m}&{l}{a}{n}\ge&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{F}{e}{m}{a}\le&{58}&{63}&{17}&{138}\backslash{M}{a}\le&{79}&{61}&{25}&{165}\backslash{T}{o}{t}{a}{l}&{137}&{124}&{42}&{303}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ?

2020-11-08
1) Given data table , $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{G}{e}{n}{d}{e}{r}\backslash{h}{l}\in{e}{A}{f}{f}{i}{l}{i}{a}{t}{i}{o}{n}&{M}{a}\le&{F}{e}{m}{a}\le&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{D}{e}{m}{o}{c}{r}{a}{t}&{300}&{600}&{900}\backslash{h}{l}\in{e}{R}{e}{p}{u}{b}{l}{i}{c}{a}{n}&{500}&{300}&{800}\backslash{h}{l}\in{e}{O}{t}{h}{e}{r}&{200}&{100}&{300}\backslash{h}{l}\in{e}{T}{o}{t}{a}{l}&{1000}&{1000}&{2000}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ Number of all voters male and registered as a democrat x = 300 Total voters = n = 2000 Proportion of all voters is male and registered as democrat is , PSK\frac{x}{n} = \frac{300}{2000} = 0.15 2) Given data table, $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{S}{i}{z}{e}\ {o}{f}\ {C}{a}{r}\backslash{h}{l}\in{e}{G}{e}{n}{d}{e}{r}&{S}{m}{a}{l}{l}&{M}{e}{d}{i}{u}{m}&{l}{a}{n}\ge&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{F}{e}{m}{a}\le&{58}&{63}&{17}&{138}\backslash{M}{a}\le&{79}&{61}&{25}&{165}\backslash{T}{o}{t}{a}{l}&{137}&{124}&{42}&{303}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ The marginal distribution of car size, $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{S}{i}{z}{e}\ {o}{f}\ {c}{a}{r}&{s}{m}{a}{l}{l}&{m}{e}{d}{i}{u}{m}&{l}{a}{r}\ge&\to{t}{a}{l}\backslash{h}{l}\in{e}{P}{r}{o}{b}{a}{b}{i}{l}{i}{t}{y}&{\frac{{{137}}}{{{303}}}}={0.452}&{\frac{{{124}}}{{{303}}}}={0.409}&{\frac{{{42}}}{{{303}}}}={0.137}&{1}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ In the marginal distribution for car size, the entry for medium cars is 0.409

### Relevant Questions

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.
A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below.
$$\begin{array}{c|cccc|c} & \text {Winter} &\text{Spring}& \text {Summer } & \text {Fall}& \text {Total}\\ \hline \text {Children} & 30 & 0 & 170&0&200 \\ \text{Teens} & 150 & 75 & 250&25&500 \\ \text {Adults } & 250 & 250 & 250&250&1000 \\ \text {Seniors} & 300 & 150 & 50&300&800 \\ \hline \text {Total} & 730 & 475 & 720 &575&2500 \end{array}$$
Among those whose favorite season is spring, what proportion are adults?
$$a) \frac{250}{1000}$$
$$b) \frac{250}{2500}$$
$$c) \frac{475}{2500}$$
$$d) \frac{250}{475}$$
$$e) \frac{225}{475}$$
Gastroenterology
We present data relating protein concentration to pancreatic function as measured by trypsin secretion among patients with cystic fibrosis.
If we do not want to assume normality for these distributions, then what statistical procedure can be used to compare the three groups?
Perform the test mentioned in Problem 12.42 and report a p-value. How do your results compare with a parametric analysis of the data?
Relationship between protein concentration $$(mg/mL)$$ of duodenal secretions to pancreatic function as measured by trypsin secretion:
$$\left[U/\left(k\ \frac{g}{h}r\right)\right]$$
Tapsin secreton [UGA]
$$\leq\ 50$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.7 \\ \hline 2 & 2.0 \\ \hline 3 & 2.0 \\ \hline 4 & 2.2 \\ \hline 5 & 4.0 \\ \hline 6 & 4.0 \\ \hline 7 & 5.0 \\ \hline 8 & 6.7 \\ \hline 9 & 7.8 \\ \hline \end{array}$$
$$51\ -\ 1000$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.4 \\ \hline 2 & 2.4 \\ \hline 3 & 2.4 \\ \hline 4 & 3.3 \\ \hline 5 & 4.4 \\ \hline 6 & 4.7 \\ \hline 7 & 6.7 \\ \hline 8 & 7.9 \\ \hline 9 & 9.5 \\ \hline 10 & 11.7 \\ \hline \end{array}$$
$$>\ 1000$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 2.9 \\ \hline 2 & 3.8 \\ \hline 3 & 4.4 \\ \hline 4 & 4.7 \\ \hline 5 & 5.5 \\ \hline 6 & 5.6 \\ \hline 7 & 7.4 \\ \hline 8 & 9.4 \\ \hline 9 & 10.3 \\ \hline \end{array}$$
A random sample of $$\displaystyle{n}_{{1}}={16}$$ communities in western Kansas gave the following information for people under 25 years of age.
$$\displaystyle{X}_{{1}}:$$ Rate of hay fever per 1000 population for people under 25
$$\begin{array}{|c|c|} \hline 97 & 91 & 121 & 129 & 94 & 123 & 112 &93\\ \hline 125 & 95 & 125 & 117 & 97 & 122 & 127 & 88 \\ \hline \end{array}$$
A random sample of $$\displaystyle{n}_{{2}}={14}$$ regions in western Kansas gave the following information for people over 50 years old.
$$\displaystyle{X}_{{2}}:$$ Rate of hay fever per 1000 population for people over 50
$$\begin{array}{|c|c|} \hline 94 & 109 & 99 & 95 & 113 & 88 & 110\\ \hline 79 & 115 & 100 & 89 & 114 & 85 & 96\\ \hline \end{array}$$
(i) Use a calculator to calculate $$\displaystyle\overline{{x}}_{{1}},{s}_{{1}},\overline{{x}}_{{2}},{\quad\text{and}\quad}{s}_{{2}}.$$ (Round your answers to two decimal places.)
(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use $$\displaystyle\alpha={0.05}.$$
(a) What is the level of significance?
State the null and alternate hypotheses.
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}<\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}>\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}\ne\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}>\mu_{{2}},{H}_{{1}}:\mu_{{1}}=\mu_{{12}}$$
(b) What sampling distribution will you use? What assumptions are you making?
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,
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations,
The Student's t. We assume that both population distributions are approximately normal with known standard deviations,
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimalplaces.)
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
P-value $$\displaystyle>{0.250}$$
$$\displaystyle{0.125}<{P}-\text{value}<{0},{250}$$
$$\displaystyle{0},{050}<{P}-\text{value}<{0},{125}$$
$$\displaystyle{0},{025}<{P}-\text{value}<{0},{050}$$
$$\displaystyle{0},{005}<{P}-\text{value}<{0},{025}$$
P-value $$\displaystyle<{0.005}$$
Sketch the sampling distribution and show the area corresponding to the P-value.
P.vaiue Pevgiue
P-value f P-value
At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September: $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}&{C}{r}{a}{w}{l}\in{g}\ {a}\ge\backslash{h}{l}\in{e}{B}{i}{r}{t}{h}\ {m}{o}{n}{t}{h}&{M}{e}{a}{n}&{S}{t}.{d}{e}{v}.&{n}\backslash{h}{l}\in{e}{J}{a}\nu{a}{r}{y}&{29.84}&{7.08}&{32}\backslash{M}{a}{y}&{28.58}&{8.07}&{27}\backslash{S}{e}{p}{t}{e}{m}{b}{e}{r}&{33.83}&{6.93}&{38}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ Crawling age is given in weeks. Assume the data represent three independent simple random samples, one from each of the three populations consisting of babies born in that particular month, and that the populations of crawling ages have Normal distributions. A partial ANOVA table is given below. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{S}{o}{u}{r}{c}{e}&{S}{u}{m}\ {o}{f}\ \boxempty{s}&{D}{F}&{M}{e}{a}{n}\ \boxempty\ {F}\backslash{h}{l}\in{e}{G}{r}{o}{u}{p}{s}&{505.26}\backslash{E}{r}{r}{\quad\text{or}\quad}&&&{53.45}\backslash{T}{o}{t}{a}{l}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ What are the degrees of freedom for the groups term?
The following is a two-way table showing preferences for an award (A, B, C) by gender for the students sampled in survey. Test whether the data indicate there is some association between gender and preferred award.
$$\begin{array}{|c|c|c|}\hline &\text{A}&\text{B}&\text{C}&\text{Total}\\\hline \text{Female} &20&76&73&169\\ \hline \text{Male}&11&73&109&193 \\ \hline \text{Total}&31&149&182&360 \\ \hline \end{array}\\$$
Chi-square statistic=?
p-value=?
Conclusion: (reject or do not reject $$H_0$$)
Does the test indicate an association between gender and preferred award? (yes/no)
Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.
$$\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 200 & 53.00\\ \hline 250 & 52.50\\\hline 300 & 52.00\\ \hline 350 & 51.50\\ \hline \end{array}$$
(a) Find a formula for p in terms of N modeling the data in the table.
$$\displaystyle{p}=$$
(b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.
$$\displaystyle{R}=$$
Is R a linear function of N?
(c) On the basis of the tables in this exercise and using cost, $$\displaystyle{C}={35}{N}+{900}$$, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month.
$$\displaystyle{P}=$$
(d) Is P a linear function of N?
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.
$$\begin{array}{c|ccc|c} &\text { Green } & \text { Blue }& \text { Yellow }& \text { Total }\\ \hline \text{ Male } & 40&24&16&80\\ \text{ Female} &30&60&30&120\\ \hline \text{Total}&70&84&46&200 \end{array}\$$