Engineers concerned about a tower's stability have done extensive studies of its increasing tilt. Measurements of the lean of the tower over time provide much useful information. The following table gives measurements for the years 1975 to 1987. The variable "lean" represents the difference between where a point on the tower would be if the tower were straight and where it actually is. The data are coded as tenths of a millimeter in excess of 2.9 meters, so that the 1975 lean, which was 2.9644 meters, appears in the table as 644. Only the last two digits of the year were entered into the computer.

Year 75 76 77 78 79 80 81 82 83 84 85 86 87

Lean 644 646 657 668 675 690 698 700 715 718 726 743 759

(a) Plot the data. Consider whether or not the trend in lean over time appears to be linear. (Do this on paper. Your instructor may ask you to turn in this graph.) (b) What is the equation of the least-squares line? (Round your answers to three decimal places.) y = + x What percent of the variation in lean is explained by this line? (Round your answer to one decimal place.) % (c) Give a 99% confidence interval for the average rate of change (tenths of a millimeter per year) of the lean. (Round your answers to two decimal places.) ( , )

2. Your local grocery store claims that on average their fresh caught salmon will weigh 2 pounds. You want to test to see if their claim is correct so you gather a simple random sample of 45 packages of their fresh caught salmon, weigh each package, and find that the average weight of these packages is 1.76 pounds. Based on years of data, the grocery store determined that the standard deviation ? = 0.08 pounds. What is the probability of obtaining the sample that you got? Do you think the grocery store is wrong to say that on average their packages of salmon weigh 2 pounds? Why or why not?

John knows that monthly demand for his product follows a normal distribution with a mean of 2,500 units and a standard deviation of 425 units. Given this, please provide the following answers for John.

a. What is the probability that in a given month demand is less than 3,000 units?

b. What is the probability that in a given month demand is greater than 2,200 units?

c. What is the probability that in a given month demand is between 2,200 and 3,000 units?

d. What is the probability that demand will exceed 5,000 units next month?

e. If John wants to make sure that he meets monthly demand with production output at least 95% of the time. What is the minimum he should produce each month?

Show in excel with formulas

Spertus et al. performaed a randomized single blind study for subjects with stable coronary artery disease. They randomized subjects into two treatments groups. The first group had current angina medications optimized and the second group was tapered off existing medications and then started on long-acting diltiazem at 180mg/day. The researchers performed several tests to determine if there were significant differences in the two treatment groups at baseline. One of the characteristics of interest was the difference in the percentages of subjects who had reported a history of congestive heart failure. In the group where current medications were optimized, 16 of 49 subjects reported a history of congestive heart failure. The subjects placed on the diltiazem, 12 of the 51 subjects reported a history of congestive heart failure. What is the hypothesis and the conclusion?

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.2 ounces and a standard deviation of 1.3 ounces.

(a) If 4 potatoes are randomly selected, find the probability that the mean weight is less than 10.0 ounces. Round your answer to 4 decimal places.

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.6 ounces. Round your answer to 4 decimal places.

Determine the factorization method and MLE of gamma distribution

Pay your taxes: According to the Internal Revenue Service, the proportion of federal tax returns for which no tax was paid was =p0.326. As part of a tax audit, tax officials draw a simple sample of =n140 tax returns. Use Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

Part 1 of 4

(a)What is the probability that the sample proportion of tax returns for which no tax was paid is less than 0.29?

Part 2 of 4

(b)What is the probability that the sample proportion of tax returns for which no tax was paid is between 0.36 and 0.43?

Part 3 of 4

(c)What is the probability that the sample proportion of tax returns for which no tax was paid is greater than 0.32?

Part 4 of 4

(d)Would it be unusual if the sample proportion of tax returns for which no tax was paid was less than 0.23?

Descriptive statistics: What do all of those numbers mean in terms of the problem. Organizing and summarizing data is called descriptive statistics. Two ways to summarize data are by graphing and by using numbers (for example, finding an average). A statistical graph is a tool that helps you learn about the shape or distribution of a sample or a population. Our data is examining the distance (miles) between twenty retail stores, and a large distribution center The Mean: (84.05 miles) shows the arithmetic mean of the sample data. Standard E: (7.71822 miles) shows the standard error of the data set, which is the difference between the predicted value and the actual value. Median: (86.5 miles) shows the middle value in the data set, which is the value that separates the largest half of the values from the smallest half of the values Mode: (96 miles) shows the most common value in the data set. Standard [: (34.51693 miles) shows the sample standard deviation measure for the data set. Sample Va: (1191.418 miles) shows the sample variance for the data set, the squared standard deviation. Kurtosis: (-0.48156 miles) shows the kurtosis of the distribution. Skewness: (0.210738 miles) shows the skewness of the data set’s distribution. Range: (121 miles) shows the difference between the largest and smallest values in the data set. Minimum: ( 29 miles) shows the smallest value in the data set. Maximum: (150 miles) shows the largest value in the data set. Sum (1681 miles) adds all the values in the data set together to calculate the sum. Count (20 miles) counts the number of values in a data set.

-Identify why you choose to perform the statistical test (Sign test, Wilcoxon test, Kruskal-Wallis test).

-Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.

-Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

-Find the critical value(s) and identify the rejection region(s).

-Find the appropriate standardized test statistic. If convenient, use technology.

-Decide whether to reject or fail to reject the null hypothesis.

-Interpret the decision in the context of the original claim.

A weight-lifting coach claims that weight-lifters can increase their strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. Thirty days later, after regular training supplemented by vitamin E, they are tested again. The results are listed below. Use the Wilcoxon signed-rank test to test the claim that the vitamin E supplement is effective in increasing athletes' strength. Use α = 0.05.

A recent Pew Center Research survey revealed that 68% of high school students have used tobacco related products. Suppose a statistician randomly selected 20 high school students. Use this information to answer questions 39-41.

1. To find the probability that exactly 15 used tobacco products, would you use the Binomial, Geometric, or Poisson distribution to find the probability?
2. Set up the problem to find P (X = 15) using the appropriate distribution. Do NOT solve.
3. What is the expected number of high school students in the sample who have used tobacco products?

For a self check out at the local Walmart, the mean number of customers per 5 minute interval is 1.5 customers. Use this information to answer questions 42 and 43.

1. To find the probability of 2 customers in the next 5 minutes, would you use the Binomial, Geometric, or Poisson distribution to find the probability?
2. What is the variance (numeric value)?  

Assuming the grades on the first homework are nearly normal with N(90, 4.3), what proportion of grades fall between 85 and 90?
Assuming the grades on the final exam are nearly normal with N(90, 4.3), for a grade of 95 or more on the exam, find the z-score and explain what it means.
Assuming the grades on the final exam are nearly normal with N(90, 4.3), what is the minimum grade putting you in the top 15% of the class?
Assuming the grades on the final exam are nearly normal with N(82, 3.86), what proportion of grades fall between 85 and 90?

The Data

The real estate markets, around the United States, have been drastically changing since the housing crisis of 2008. Many experts agree that there has never been a time where the market was so friendly to low interests rates and home prices for prospective buyers. Your task, in this project, is to investigate the housing market in the county that you current reside.

Objective 1 (35 points)

Using the website, www.zillow.com, randomly select 35 homes and record the price of each home. In the space below, clearly define how you randomly selected these homes and provide a table with the home costs you selected.

Answer= I selected these homes in the area code from which I reside within a 25 mile radius. The homes selected were the ones listed as the newest houses on zillow.

Objective 2 (20 points)

• Compute the following:

The average home price for your sample

The standard deviation home price

• Using complete sentences, define the random variable .

• State the estimated distribution to use. Use complete sentences and symbols where appropriate.

Objective 3 (20 points)

Respond to each of the following

• Calculate the 90% confidence interval and the margin of error.

• Interpret this confidence interval.

Objective 4 (25 points)

Using your data set, calculate four additional confidence intervals and margins of error at the levels of confidence given below:

• 50%

• 80%

• 95%

• 99%

What happens to the margin of error as the confidence level increases? Does the width of the confidence interval increase or decrease? Explain why this happens.

Have we learned from past mortgage mistakes? Are the practices and the products that caused the mortgage crisis gone? How is the current stance of the mortgage markets and mortgage borrowing? What are some examples of practices and approaches adopted by the government and the mortgage industry to revive the market after the subprime mortgage crisis?

A five (5) page Reflective Journal reflecting on the processes which can be utilised to collect data while conducting research as well as on tools to analyse data collected in the research process.