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.

The price of a gallon of milk at 16 randomly selected Arizona stores is given below. Assume that milk prices are normally distributed. At the α=0.10α=0.10 level of significance, is there enough evidence to conclude that the mean price of a gallon of milk in Arizona is less than $3.00? (Round your results to three decimal places)

Which would be correct hypotheses for this test?

• H0:μ=$3H0:μ=$3, H1:μ≠$3H1:μ≠$3
• H0:μ=$3H0:μ=$3, H1:μ>$3H1:μ>$3
• H0:μ≠$3H0:μ≠$3, H1:μ=$3H1:μ=$3
• H0:μ<$3H0:μ<$3, H1:μ=$3H1:μ=$3
• H0:μ=$3H0:μ=$3, H1:μ<$3H1:μ<$3

Gallon of Milk prices:

test statistic:



Give the P-value:

If X is a normal random variable with parameters σ2 = 36 and μ = 10, compute (a) P{X ≥ 5} .
(b) P{X = 5}.
(c) P{10>X≥5}.
(d) P{X < 5}.
(e) Find the y such that P{X > y} = 0.1.

For a standard normal distribution, what is the probability that z is greater than 1.65

In a recent issue of Consumer Reports, Consumers Union reported on their investigation of bacterial contamination in packages of name brand chicken sold in supermarkets. Packages of Tyson and Perdue chicken were purchased. Laboratory tests found campylobacter contamination in 35 of the 75 Tyson packages and 22 of the 75 Perdue packages.

Question 1. Find 90% confidence intervals for the proportion of Tyson packages with contamination and the proportion of Perdue packages with contamination (use 3 decimal places in your answers).

_____ lower bound of Tyson interval

_____ upper bound of Tyson interval

_____ lower bound of Perdue interval

_____ upper bound of Perdue interval

Question 2. The confidence intervals in question 1 overlap. What does this suggest about the difference in the proportion of Tyson and Perdue packages that have bacterial contamination? One submission only; no exceptions

The overlap suggests that there is no significant difference in the proportions of packages of Tyson and Perdue chicken with bacterial contamination.

Even though there is overlap, Tyson's sample proportion is higher than Perdue's so clearly Tyson has the greater true proportion of contaminated chicken.

Question 3. Find the 90% confidence interval for the difference in the proportions of Tyson and Perdue chicken packages that have bacterial contamination (use 3 decimal places in your answers).

_____ lower bound of confidence interval

_____ upper bound of confidence interval

Question 4. What does this interval suggest about the difference in the proportions of Tyson and Perdue chicken packages with bacterial contamination? One submission only; no exceptions

We are 90% confident that the interval in question 3 captures the true difference in proportions, so it appears that Tyson chicken has a greater proportion of packages with bacterial contamination than Perdue chicken.

Natural sampling variation is the only reason that Tyson appears to have a higher proportion of packages with bacterial contamination.

Tyson's sample proportion is higher than Perdue's so clearly Tyson has the greater true proportion of contaminated chicken.

Question 5. The results in questions 2 and 4 seem contradictory. Which method is correct: doing two-sample inference, or doing one-sample inference twice? One submission only; no exceptions

two-sample inference

one-sample inference twice

Question 6. Why don't the results agree? 2 submission only; no exceptions

The one- and two-sample procedures for analyzing the data are equivalent; the results differ in this problem only because of natural sampling variation.

If you attempt to use two confidence intervals to assess a difference between proportions, you are adding standard deviations. But it's the variances that add, not the standard deviations. The two-sample difference-of-proportions procedure takes this into account.

Different methods were used in the two samples to detect bacterial contamination.

Tyson chicken is sold in less sanitary supermarkets.

Which of the following variables yields data that would be suitable for use in a histogram? __________

Problem 6: Researchers are testing two new cholesterol medications. Medication is given to some males and females and a placebo is given to others. The tablesbelow summarize the resulting HDL cholesterol levels after 8 weeks.

Problem 6a: Is there evidence of effect modification with medication A? Provide a brief (1-2 sentences) explanation.

Problem 6b: Is there evidence of effect modification with medication B? Provide a brief (1-2 sentences) explanation.