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.

The ages of a group of 135 randomly selected adult females have a standard deviation of 17.9 years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let sigmaequals17.9 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics​ students? Assume that we want 95​% confidence that the sample mean is within​ one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general​ population?

1. A consumer group is testing camp stoves. To test the heating capacity of a stove, they measure the time required to bring 2 quarts of water from 50 degrees to boiling.

Two competing models are under consideration. Thirty-six stoves of each model were tested and the following results were obtained.

     Model 1: mean time is 11.4 and standard deviation is2.5

     Model 2: mean time is   9.9 and standard deviation is 3.0

1. Is there any difference between the performances of these two models? {use a .05 level of significance}. Find the p-value of the sample statistic and do a significance test.
2. Find a 95% confidence interval for the difference of the means.

2. a. Use signifcance test to test the indicated claim. A standard aptitude test is given to several randomly selected programmers, and the scores are given below for the mathematics and verbal portions of the test. At the 0.05 level of significance, test the claim that programmers do better on the mathematics portion of the test.

               Mathematics 447 540 427 456 527 449 477 498 425         

               Verbal                    385 478 343 371 440 371 394 422 385

b. Find a 90% confidence interval for the difference of the mean.

What criteria would you look at when conducting a statistical analysis to determine which online dating site(s) someone should use, and why? If you would not consider online dating for yourself, ask a friend who has been or is participating in online dating for their input. For example, do you think it is necessary to simply fill in the answers in the profile, such as height, body type, hair color, etc., and your preferences in these same categories for your match? Or do you think it is also necessary to answer the questions that can help find someone who may be more suited to your personality? These types of questions cover a variety of genres, such as relationships, sex, politics and law, and life and death.4 You can also find information online about statistics indicating which site yields the most success. Success may be determined by the site that yields the most number of dates, or the most marriages. In your response, share with your peers what success determinate you found or looked for. What sample size do you think you would need to determine which site is most likely to yield the greatest success? In your response, please provide a link to an article about dating sites or a link to dating site that explains what kind of data these sites provide.

A study found that the mean amount of time cars spent in​ drive-throughs of a certain​ fast-food restaurant was

157.6157.6

seconds. Assuming​ drive-through times are normally distributed with a standard deviation of

3434

​seconds, complete parts​ (a) through​ (d) below.Click here to view the standard normal distribution table (page 1).

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Click here to view the standard normal distribution table (page 2).

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​(a) What is the probability that a randomly selected car will get through the​ restaurant's drive-through in less than

118118

​seconds?The probability that a randomly selected car will get through the​ restaurant's drive-through in less than

118118

seconds is

nothing.

​(Round to four decimal places as​ needed.)

​(b) What is the probability that a randomly selected car will spend more than

210210

seconds in the​ restaurant's drive-through?The probability that a randomly selected car will spend more than

210210

seconds in the​ restaurant's drive-through is

nothing.

​(Round to four decimal places as​ needed.)

​(c) What proportion of cars spend between

22

and

33

minutes in the​ restaurant's drive-through?The proportion of cars that spend between

22

and

33

minutes in the​ restaurant's drive-through is

nothing.

​(Round to four decimal places as​ needed.)

​(d) Would it be unusual for a car to spend more than

33

minutes in the​ restaurant's drive-through?​ Why?