Explain the following issues using diagram (Graphs)

a) Relationship between f(x) and F(x) for a continuous variable,

b) explaining how a uniform random variable can be used to simulate X via the cumulative distribution function of X, or

c) explaining the effect of transformation on a discrete and/or continuous random variable

Please do not use this as an example: For example, let’s say you had four groups, representing drugs A B C D, with each group composed of 20 people in each group and you’re measuring people’s cholesterol level.

In your own words, describe the difference between Among Group Variation and Within Group Variation. Discuss how you would evaluate the variation and other methods to ensure that the data is appropriate to use for the test. Illustrate using a specific example.

At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of n1 = 324 patients with minor burns received the plasma compress treatment. Of these patients, it was found that 268 had no visible scars after treatment. Another random sample of n2 = 418 patients with minor burns received no plasma compress treatment. For this group, it was found that 93 had no visible scars after treatment. Let p1 be the population proportion of all patients with minor burns receiving the plasma compress treatment who have no visible scars. Let p2 be the population proportion of all patients with minor burns not receiving the plasma compress treatment who have no visible scars. (a) Find a 90% confidence interval for p1 − p2. (Round your answers to three decimal places.) lower limit upper limit (b) Explain the meaning of the confidence interval found in part (a) in the context of the problem. Does the interval contain numbers that are all positive? all negative? both positive and negative? At the 90% level of confidence, does treatment with plasma compresses seem to make a difference in the proportion of patients with visible scars from minor burns? Because the interval contains only negative numbers, we can say that there is a higher proportion of patients with no visible scars among those who did not receive the treatment. Because the interval contains only positive numbers, we can say that there is a higher proportion of patients with no visible scars among those who received the treatment. We can not make any conclusions using this confidence interval. Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of patients with no visible scars among those who received the treatment.

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 467 eggs in group I boxes, of which a field count showed about 266 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 786 eggs in group II boxes, of which a field count showed about 270 hatched. (a) Find a point estimate p̂1 for p1, the proportion of eggs that hatch in group I nest box placements. (Round your answer to three decimal places.) p̂1 = Find a 90% confidence interval for p1. (Round your answers to three decimal places.) lower limit upper limit (b) Find a point estimate p̂2 for p2, the proportion of eggs that hatch in group II nest box placements. (Round your answer to three decimal places.) p̂2 = Find a 90% confidence interval for p2. (Round your answers to three decimal places.) lower limit upper limit (c) Find a 90% confidence interval for p1 − p2. (Round your answers to three decimal places.) lower limit upper limit Does the interval indicate that the proportion of eggs hatched from group I nest boxes is higher than, lower than, or equal to the proportion of eggs hatched from group II nest boxes? Because the interval contains both positive and negative numbers, we can not say that a higher proportion of eggs hatched in well-separated and well-hidden nesting boxes. Because the interval contains only positive numbers, we can say that a higher proportion of eggs hatched in well-separated and well-hidden nesting boxes. Because the interval contains only negative numbers, we can say that a higher proportion of eggs hatched in highly visible, closely grouped nesting boxes. We can not make any conclusions using this confidence interval. (d) What conclusions about placement of nest boxes can be drawn? In the article discussed in the Focus Problem, additional concerns are raised about the higher cost of placing and maintaining group I nest box placements. Also at issue is the cost efficiency per successful wood duck hatch. No conclusion can be made. A greater proportion of wood duck eggs hatch if the eggs are laid in well-separated, well-hidden nesting boxes. A greater proportion of wood duck eggs hatch if the eggs are laid in highly visible, closely grouped nesting boxes. The eggs hatch equally well in both conditions.

Your power plant emits nitrous oxides (NOx) into the atmosphere as a byproduct of burning coal. While your scrubbers collect much of the pollutant before it leaves your smokestacks, they cannot get it all. You have an allowance of one hundred pounds of NOx per day. The state environmental commission shows up periodically to test whether you are staying within your allowance. If you are not within your allowance, you will have to purchase more allowance from a plant that is not using all of theirs (a costly proposition). You periodically test your smoke to see how things are going. The numbers in the table represent a test of n = 10 randomly selected days over the past month.

a. Construct a 95% confidence interval for your average daily pounds of pollutants.

b. Should you be worried? Why, why not?  

What are some of the limitations of using Excel for pivot tables/charts? Why does that make software like Tableau more appealing in the workplace?

The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.1 5.6 6.2 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.7 5.1 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.6 1.9 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.4 1.7 1.0 1.7 1.9 1.6 1.4 1.5 1.4 1.2 1.3 1.5 1.3 1.6 1.9 1.4 1.6 1.5 1.4 1.6 1.2 1.9 1.5 1.6 1.4 1.3 1.7 1.5 1.5 (a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 99% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit (c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, is the population mean petal length of Iris virginica longer than that of Iris setosa? Because the interval contains only positive numbers, we can say that the mean petal length of Iris virginica is longer. Because the interval contains only negative numbers, we can say that the mean petal length of Iris virginica is shorter. Because the interval contains both positive and negative numbers, we cannot say that the mean petal length of Iris virginica is longer. (d) Which distribution did you use? Why? The Student's t-distribution was used because σ1 and σ2 are unknown. The standard normal distribution was used because σ1 and σ2 are known. The standard normal distribution was used because σ1 and σ2 are unknown. The Student's t-distribution was used because σ1 and σ2 are known. Do you need information about the petal length distributions? Explain. Both samples are large, so information about the distributions is needed. Both samples are large, so information about the distributions is not needed. Both samples are small, so information about the distributions is needed. Both samples are small, so information about the distributions is not needed.

any state auto insurance company took a random sample of 360 insurance claims paid out during a one year. The average claim paid was $1,575 assume the name equals $238 find a 0.90 confidence interval for the mean claim round your answers to two decimal places lower limit of the find a 0.99 confidence interval for the mean claim payment round your answers to two decimal places lower limit upper limit

Data are gathered on each car in the motor pool, regarding number of miles (in thousand miles) driven in a given year, and maintenance costs (in thousand dollars) for that year:

Part of the linear regression analysis output are shown in below:

3. Construct a 95% confidence interval for the conditional mean of y given x0=50.

   (A) [2.476, 2.879]   (B) [1.538, 2.409] (C) [1.651, 2.30] (D) [2.410, 2.908]

3. Construct a 95% prediction interval at x0=50.

(A) [2.360, 2.996]

(B) [2.064, 3.254]

(C) [1.612, 2.335]

(D) [2.223, 3.132]

The Apex corporation produces corrugated paper. It has collected monthly data from January 2001 through March 2003 on the following two variables:

y= total manufacturing cost per month (In thousands of dollars) (COST)

x= total machine hours used per month (Machine)

The data are shown below.

1102 218
1008 199
1227 249
1395 277
1710 363
1881 399
1924 411
1246 248
1255 259
1314 266
1557 334
1887 401
1204 238
1211 246
1287 259
1451 286
1828 389
1903 404
1997 430
1363 271
1421 286
1543 317
1774 376
1929 415
1317 260
1302 255
1388 281

answer the following questions

a. State the least squares regression line.

b. What percentage of variation in ? has been explained by the regression?

c. Are ? and ? linearly related? Conduct a hypothesis test at the 5% significance level by completing the following steps:

i. State the null and alternative hypotheses

ii. State the value of the test statistic

iii. Provide the p-value

iv. Do you reject the null hypothesis or not? Explain your answer.

v. State you conclusion within context of the problem.

d. Fill in the blanks for the following statement: “I am 95% confident that the average manufacturing cost at the Apex corporation for all months with 350 total machine hours is between ____ and ____.”

Please show me the steps. Thank you

Thirty-two small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 41.3 cases per year. (a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit upper limit margin of error (b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit upper limit margin of error (c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit upper limit margin of error (d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase? As the confidence level increases, the margin of error decreases. As the confidence level increases, the margin of error increases. As the confidence level increases, the margin of error remains the same. (e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length? As the confidence level increases, the confidence interval decreases in length. As the confidence level increases, the confidence interval increases in length. As the confidence level increases, the confidence interval remains the same length.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 41 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.94 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.41 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

Thirty-four small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 44.3 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error increases.As the confidence level increases, the margin of error decreases.    As the confidence level increases, the margin of error remains the same.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval increases in length.As the confidence level increases, the confidence interval decreases in length.    As the confidence level increases, the confidence interval remains the same length.

How would we determine the right comparative method to use when analyzing the different studies that we are interested in using in our research?

Numerous studies have shown that IQ scores have been increasing, generation by generation, for years (Flynn, 1984, 1999). The increase is called the Flynn Effect, and the data indicate that the increase appears to be about 7 points per decade. To demonstrate this phenomenon, a researcher obtains an IQ test that was written in 1980. At the time the test was prepared, it was standardized to produce a population mean of 100. The researcher administers the test to a random sample of 16 of today's high school students and obtains a sample mean IQ of 110 with standard deviation of 20. Is this result sufficient to conclude that today's sample scored significantly higher than would be expected from a population with 100? Test this claim at the 5% significance level.

Fill in the blanks with the appropriate responses:

Hypotheses
H₀: The mean IQ score is 100
H₁: The mean IQ score is Blank 1 100
(type in “less than”, “greater than”, or “not equal to”)

Results
t = Blank 2 (enter the test statistic, use 2 decimal places)
p-value = Blank 3 (round answer to nearest thousandth of a percent – i.e. 0.012%)

Conclusion
We Blank 4 sufficient evidence to support the claim that the mean IQ is Blank 5 100 (p Blank 6 0.05).
(Use “have” or “lack” for the first blank, “less than”, “greater than” or “not equal to” for the second blank and “<” or “>” for the final blank)

1) The daily demand, D, of sodas in the break room is:

i) Find the probability that the demand is at most 2.
ii) Compute the average demand of sodas.
iii) Compute SD of daily demand of sodas.

2) From experience you know that 83% of the desks in the schools have gum stuck
beneath them. In a random sample of 14 desks.
a) Compute the probability that all of them have gum underneath.
b) Compute the probability that 10 or less desks have gum.
c) What is the probability that more than 10 have gum?
d) What is the expected number of desks in the sample have gum?
e) What is the SD of the number of desks with gum?

3) The number of customers, X, arriving in a ATM in the afternoon can be modeled
using a Poisson distribution with mean 6.5.
a) Compute P(X<3).
b) Compute P(X>4).
c) SD of X.