1. Empirical probability: A statistical model was developed to predict whether passengers on the Titanic ship survived base on their information such as age, number of siblings and spouses were on the ship, sex, the fare class, etc. The table below presents the predicted results getting from the model compared with the actual record:

1. If picking a random passenger, what is the probability that the passenger survived according to the model or predicted by the model?

2. If picking a random passenger, what is the probability that the passenger did not survive according to the real record?

3. If a passenger was predicted as a survivor, what is the probability that the passenger actually survived according to the actual record?

4. If a passenger was predicted as a non-survivor, what is the probability that the passenger actually did not survive according to the actual record?  

2. You are conducting a statistical study in order to estimate the average number of people who have contacted a patient with a positive test for the COVID-19 virus in the US over the last three weeks. Describe a detailed plan for collecting the data for your study. Your answer should be in paragraph​        form and be sure to include the following information:  
   1. The target population
   2. The study variable(s); the variable(s)’s type (quantitative or qualitative); the variable(s)’s level of measurement (nominal, ordinal, interval, or ratio)
   3. The study sample:
      1. Your sample size
      2. Data collection method (survey, simulation, etc)
      3. Sample technique (clustered, stratified, simple random, etc)
      4. Possible errors if any  

In Lesson Seven you've learned to convert raw scores to standard scores and used the empirical rule to determine probabilities associated with those standard scores.

Random Decimal Fraction Generator

Here are your random numbers:

0.1613
0.8590
0.7911

1. Use the random decimal fraction generator at Random.org, linked here, to generate a list of three fractions with four decimal places(LIST random decimal fraction generator  IS ON TOP). Assume those decimal fractions represent probability values associated with z-scores. Then use the standard normal table to look up the z-score that is closest to matching with that probability. List them below. (3 points)
   1. probability value (generated fraction) =
   2. associated z-score =
   3. probability value (generated fraction) =
   4. associated z-score =
   5. probability value (generated fraction) =
   6. associated z-score =
2. Use another random decimal fraction generator at Random.org, linked here, to generate a list of ten two-digit random numbers between 10 and 30. Calculate the z-score of the median of the data set. (3 points)
3. What does the z-score of the data set median just above tell you about the shape of the distribution? How do you know this? (3 points)
4. If you were to take repeated random samples of n = 5 from the data set just above, what would be the expected value of the mean of the sampling distribution of sample means? (3 points)
5. Considering the set of ten two-digit random numbers above as a population, calculate the standard error of the mean for the samples in question 4. (3 points)

The compounds listed here are often found in many natural flavors and scents. Calculate the empirical formula for each compound.

ethyl butyrate (pineapple oil): C , 62.04% ; H , 10.41% ; O , 27.55%

Express your answer as a chemical formula.

methyl butyrate (apple flavor): C , 58.80% ; H , 9.87% ; O , 31.33%

Express your answer as a chemical formula.

benzyl acetate (oil of jasmine): C , 71.98% ; H , 6.71% ; O , 21.31%

Express your answer as a chemical formula.

Construct a histogram of your empirical data using eight bars and then five bars. For consistency's sake, for eight bars use the class width of 0.125. So, your first bar will be 0.000-0.124, your next bar will be 0.125 - 0.249, etc. For five bars, use the class width of 0.2. So, your first bar will be 0.00-0.19, your next bar will be 0.2-0.39, etc. Upload both pictures of your histograms. ***Below are my 50 random numbers. What do I need to show? I am confused on what exactly I need to show. Can you help me on these?

0.9          1.0          0.7          0.0          0.8         

0.0          0.8          0.2          0.0          1.0

0.5          0.2          0.5          0.4          0.0

0.8          0.1          0.4          0.2          1.0

0.1          0.1          0.9          0.7          0.1

0.9          1.0          0.9          0.2          0.4

0.0          1.0          0.5          0.9          0.4

0.9          0.0          0.0          1.0          0.3

0.4          0.8          0.9          0.6          0.5

0.4          0.5          0.3          0.7          1.0

A Portland Cement Concrete (rigid) pavement is to be designed using AASHTO empirical design method. The pavement should have an 8" granular sub-base having elastic modulus (E_sb) of 50x10³ psi. The resilient modulus of the subgrade is 5000 psi, and lying just 5 feet above rock strata (bed rock).

(a) Determine the design k value, assuming loss of support factor (LSF) of 2.

(b) Use the k value obtained from (a) to determine the thickness of the rigid pavement.  

Assume concrete elastic modulus (E_c) = 5 x 10⁶ psi , Modulus of rupture (Sc) = 650 psi, load transfer factor J = 3.2, drainage coefficient C_d = 1.0, present serviceability loss ∆PSI = 4.2 — 2.5 = 1.7, reliability R = 95%, standard deviation S_o = 0.29, and total ESAL W₁₈ = 5.1 x 10⁶.

QUESTION 5

Never read an empirical paper without a calculator. Check the numbers and the percentages. Do the number of subjects in the tables of results add up to the numbers the researchers said they enrolled at the beginning of the study? All of this will help you understand what the authors did in conducting their study. Two other important tools to have at hand when critically reading a research paper are the highlighter tool in your word processor or spreadsheet for marking important sections of the paper and a sticky note or comment tool in your software for writing notes and questions on the paper itself.

True

False

QUESTION 7

A review of any body of literature actually consists of four fundamental tasks, after the subject of the review has been decided these include writing a synthesis that includes only the content and never a critical analysis of these materials.

True

False

QUESTION 10

A more sophisticated strategy for indexing the contents of an expanding Documents folder is the Matrix Indexing System. The simpler approach is this tracking system. Whichever system you use, the benefits accrue only if you keep the list up to date.

True

False

Empirical studies have provided support for
the belief that an ordinary share’s annual
rate of return is approximately normally
distributed. Suppose that you have invested in
the shares of a company for which the annual
return has an expected value of 16% and a
standard deviation of 10%.
a Find the probability that your one-year
return will exceed 30%.
b Find the probability that your one-year
return will be negative.
c Suppose that this company embarks on
a new, high-risk, but potentially highly
profi table venture. As a result, the return
on the share now has an expected value
of 25% and a standard deviation of 20%.
Answer parts (a) and (b) in light of the
revised estimates regarding the share’s
return.
d As an investor, would you approve of the
company’s decision to embark on the new
venture?

1. The General Social Survey polled a sample of 209 people aged 18-30 in the year 2000, asking them how many hours per week they spend on the internet. The sample mean was 6.75 with a standard deviation of 7.71. A second sample of 541 people aged 18-30 was taken in 2006. For this sample, the mean was 7.34 and standard deviation of 10.93. Assume these are simple random samples from populations of people aged 18-30. Can you conclude that the mean number of hours per week spent on the internet increased between 2000 and 2006?

a. Do the hypothesis test with α=0.05 significance level.

b. Construct a 95% confidence interval for the difference in mean number of hours spend per week on the Internet between 2000 and 2006.

c. Calculate the Margin of Error for 95% confidence level.

You are given four samples (approximately 10% oil and 90% water) all of which have been processed to have an average fat droplet size of 1.57 microns in each. They were prepared in the following manner and have different rates of separation:

Sample 1 was processed with a standard homogenizer at 2000 psi with a velocity of separation being .3 m/s

Sample 2 was processed with a standard homogenizer at 2000 psi (1^st stage) and 500 psi (2^nd stage) with a velocity of separation being .1 m/s

Sample 3 was processed with a microfluidizer with a velocity of separation being .4 m/s

Sample 4 was processed with a standard homogenizer at 2000 psi with a velocity of separation being .5 m/s (This sample had 0.5% of an emulsifier added.) THE RATE IS NOT A TYPO.

Why are the rates of separation different?