Construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place.

n=6, s=3.7, and c=0.98

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs). x 16 33 50 28 50 25 y 3 3 7 5 9 3 Complete parts (a) through (e), given Σx = 202, Σy = 30, Σx2 = 7754, Σy2 = 182, Σxy = 1162, and r ≈ 0.870. (a) Draw a scatter diagram displaying the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 5101520253035404550556012345678910 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = y hat = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained % unexplained % (f) For a neighborhood with x = 42 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.) hundred jobs

The link to the data is below, just click the link & open up the files please. Listed under MOISTURE

http://www.mediafire.com/download/thnnoaaqqefdwcf/excel_files.zip

An important quality characteristic used by the manufacturer of Boston and Vermont asphalt shingles is the amount of moisture the shingles contain when they are packaged. Customers may feel that they have purchased a product lacking in quality if they find moisture and wet shingles inside the packaging. In some cases, excessive moisture can cause the granules attached to the shingles for texture and coloring purposes to fall off the shingles, resulting in appearance problems. To monitor the amount of moisture present, the company conducts moisture tests. A shingle is weighed and then dried. The shingle is then re-weighed, and, based on the amount of moisture taken out of the product, the pounds of moisture per 100 square feet are calculated. The company would like to show that the mean moisture content is less than 0.35 pound per 100 square feet. The file Moisture includes 36 measurements ( in pounds per 100 square feet) for Boston shingles and 31 for Vermont shingles.

a. For the Boston shingles, is there evidence at the 0.05 level of significance that the population mean moisture content is less than 0.35 pound per 100 square feet?

b. Interpret the meaning of the p- value in ( a).

c. For the Vermont shingles, is there evidence at the 0.05 level of significance that the population mean moisture content is less than 0.35 pound per 100 square feet?

d. Interpret the meaning of the p- value in ( c).

e. What assumption about the population distribution is needed in order to conduct the t tests in ( a) and ( c)?

f. Construct histograms, boxplots, or normal probability plots to evaluate the assumption made in ( a) and ( c).

g. Do you think that the assumption needed in order to con-duct the t tests in ( a) and ( c) is valid? Explain.

Which of the following tables shows a valid probability density function? Select all correct answers.

Select all that apply:

• x	P(X=x)
  0	3/8
  1	1/4
  2	3/8

• x	P(X=x)
  0	0.2
  1	0.1
  2	0.35
  3	0.17

• x	P(X=x)
  0	9/10
  1	−3/10
  2	3/10
  3	1/10

• x	P(X=x)
  0	0.06
  1	0.01
  2	0.07
  3	0.86

• x	P(X=x)
  0	1/2
  1	1/8
  2	1/4
  3	1/8

• x	P(X=x)
  0	1/10
  1	1/10
  2	3/10
  3	1/5

A drug tester claims that a drug cures a rare skin disease 82​% of the time. The claim is checked by testing the drug on 100 patients. If at least 79 patients are​ cured, the claim will be accepted. Find the probability that the claim will be rejected assuming that the​ manufacturer's claim is true. Use the normal distribution to approximate the binomial distribution if possible.

Find the expected count and the contribution to the chi-square statistic for the (C,E) cell in the two-way table below

D E F G Total

A 35 30 44 41 150

B 78 90 67 58 293

C 19 38 26 32 115

Total 132 158 137 131 558

Round your answer for the expected count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Expected count =

contribution to the chi-square statistic =

In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. How large a sample should be taken if the desired margin of error is two minutes at a 95% level of confidence? How large a sample should be taken for a 99% level of confidence? Use a planning value for the population standard deviation of 7 minutes.

95% Confidence (to the nearest whole number) :

99% Confidence (to the nearest whole numer):

Given the following data set 11 20 33 45 52 30 27 21 38 42 28 25 79 60 14 35 100 23 88 58

A. Find the quartiles

B. Determine if there are any outliers

C. Draw a box plot (exclude outliers but plot them as well).

Epidemiologists claim that the probability of breast cancer among Caucasian women in their mid-60s is 0.003. An established test identified people who had breast cancer and those that were healthy. A new mammography test in clinical trials has a probability of 0.90 for detecting cancer correctly. In women without breast cancer, it has a chance of 0.975 for a negative result. If a 65-year-old Caucasian woman tests positive for breast cancer, what is the probability that she, in fact, has breast cancer?

An urn has 2 red, 5 white, and 4 blue balls in an urn and two are drawn one after another without replacement. What is the probability that the two balls are both red given that they are the same color?

Rstudio Coding Homework (submmite the pdf file to Canvas)
Let X be a Possion(λ) random variable. We have seen in class that
E(X) = Var(X) = λ.
Suppose that we do not know the true value of λ and want to estimate it from observed data {x1, x2, . . . , xn}.
There are two possible ways to do estimate λ:
• use the sample mean x¯ =
1
n
Pn
i=1 xi
• use the sample variance S
2 =
1
n−1
Pn
i=1(xi − x¯)
2
Please note that in sample variance, the denominator is n − 1 instead of n.
In this assignment, you will compare the two estimators. In the following questions, we assume that
λ = 10.
1. Generate n = 10 independent Poisson(λ) random variables, calculate the sample mean (you can use
rpois(n = ,lambda = ) function in R, where n is the total number of random varables generated and
lambda is the parameter λ). Do the above 1000 times, then you have 1000 observations of the sample
mean (each of them is calculated from n = 10 independent Poisson (λ) random variables.) Generate
the boxplot and histogram of the 1000 observation of sample means.
2. For n = 10, repeat Part 1 with the sample variance.
3. Compare the boxplot and histogram you obtained from Part 1 and 2. Comment on the difference
between them. (Hint: measure of dispersion)

---
title: "MATH 2411 Homework 2"
author: "yu wai man 20600375"
date: "2020/3/26"
output: pdf_document
#output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Coding Howework (submmite the pdf file to Canvas)
Let $X$ be a Possion$(\lambda)$ random variable. We have seen in class that $$\mathbb E(X) = \mathrm{Var}(X) = \lambda.$$ Suppose that we do not know the true value of $\lambda$ and want to estimate it from observed data $\{x_1,x_2, \dots, x_n\}$. There are two possible ways to do estimate $\lambda$:
\begin{itemize}
\item use the sample mean $\bar{x} = \frac{1}{n}\sum_{i = 1}^{n} x_i$
\item use the sample variance $S^2 = \frac{1}{n-1} \sum_{i = 1}^{n} (x_i - \bar{x})^2$
\end{itemize}
**Please note that in sample variance, the denominator is $n-1$ instead of $n$.**

In this assignment, you will compare the two estimators. **In the following questions, we assume that $\lambda = 10$.**

1. Generate $n = 10$ independent Poisson$(\lambda)$ random variables, calculate the sample mean (you can use \verb+rpois(n = ,lambda = )+ function in \verb+R+, where \verb+n+ is the total number of random varables generated and \verb+\lambda+ is the parameter $\lambda$). Do the above $1000$ times, then you have $1000$ observations of the _sample mean_ (each of them is calculated from $n=10$ independent Poisson $(\lambda)$ random variables.) **Generate the boxplot and histogram of the $1000$ observation of sample means.**

```{r sample mean}
# input your r code here

```

2. For $n = 10$, **repeat Part 1 with the _sample variance_.**

```{r sample variance}
# input your r code here

```

3. Compare the boxplot and histogram you obtained from Part 1 and 2. **Comment on the difference between them.** (Hint: measure of dispersion)

```{r boxplot and histogram}
# input your r code here

```

**Write down your comments here**

Please solve in R studio. Thanks in advance!

**Below are two samples of test scores from two different calculus classes. It is believed that class 1 performed better than class two. From previous tests it is known that the test scores for both classes are normally distributed and the population standard deviation of class 1 is 10 points and the population standard deviation of class 2 is 8 points. Do the data support that class 1 performed better.**

```{r}
class1<-c(100, 86, 98, 72, 66, 95, 93, 82)
class2<-c(98, 82, 99, 99, 70, 71, 94, 79)
```

In a particular community, 65 percent of households include at least one person who has graduated from college. You randomly sample 100 households in this community. Let X=the number of households including at least one college graduate.

What is the probability that at most 82 households include at least one college graduate?

A computer manufacturer has developed a regression model relating his sales (Y in $10,000s) with three independent variables. The three independent variables are price per unit (Price in $100s), advertising (ADV in $1,000s) and the number of product lines (Lines). Part of the regression results is shown below.

.

Note: Please write in computer typing please

Investigators interested in the association between serum vitamin D levels and various birth outcomes recruited pregnant mothers to have a blood draw during the second trimester of their pregnancy. Mothers were followed until they gave birth. The health outcomes were compared among mothers with low, adequate, and high vitamin D levels.

A) Describe the study as to its particular sampling method.

B) Describe a risk measurement that you think would be most appropriate to compare the groups, and justify your choice.

Choose the most appropriate option