College Statistics & Probability Questions and Answers

Listed below are amounts of strontium-90 (in millibecquerels or mBq per gram of calclum) in a simple random sample of baby teth obtained from resident of state A and state B. Use a 0.05 significance level to test the celm that amounts of Strontium-90 from state A residents vary more than amounts from state B resints. Assume that both samples are independent simple random samples from populations having normal distributions. $\begin{array}{cccccccccccc}StateA:& 162& 143& 150& 130& 152& 152& 143& 155& 131& 139& 164\\ StateB:& 136& 140& 142& 131& 133& 129& 141& 140& 142& 136& 142\end{array}$

A population of values has a normal distribution with ${\displaystyle \mu =198.8}$ and ${\displaystyle \sigma =69.2}$. You intend to draw a random sample of size ${\displaystyle n=147}$.
Find the probability that a single randomly selected value is between 184 and 205.1.
${\displaystyle P\left(184<X<205.1\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

If ${\displaystyle n=110}$ and ${\displaystyle \hat{p}}$ (p-hat) ${\displaystyle =0.66}$, construct a ${\displaystyle 95\mathrm{\%}}$ confidence interval. Give your answers to two decimals ${\displaystyle ?<p<?}$

A population of values has a normal distribution with ${\displaystyle \mu =239.5}$ and ${\displaystyle \sigma =32.7}$. You intend to draw a random sample of size ${\displaystyle n=139}$.
Find the probability that a sample of size $n=139$ is randomly selected with a mean greater than 235.9.
${\displaystyle P\left(M>235.9\right)=}$?
Write your answers as numbers accurate to 4 decimal places.

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
$\begin{array}{|cccccccc|}\hline 97& 91& 121& 129& 94& 123& 112& 93\\ 125& 95& 125& 117& 97& 122& 127& 88\\ \hline\end{array}$
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
$\begin{array}{|ccccccc|}\hline 94& 109& 99& 95& 113& 88& 110\\ 79& 115& 100& 89& 114& 85& 96\\ \hline\end{array}$
(i) Use a calculator to calculate ${\displaystyle {\bar{x}}_1,s_1,{\bar{x}}_2,\text{and}{s}_2.}$ (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

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 $(A\text{ and }B)=P(A)\cdot P(B)P(A\text{ and }B)=P(A)\cdot P(B).$
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.