What are distinctions between big data, applied math, (finance/ economics) and statistics?

Consider the following table of data that was generated from randomly surveying 100 people and recording how much change (from coins) was in their pockets:

1. Construct a histogram of the empirical data. Use ten "bins".Hint: It may be helpful to construct ten "bins" over the interval [0,4]

2. Construct a histogram of the empirical data. Use 20 bins.

3. Describe the shape of each graph.

The Consumer Reports National Research Center conducted a telephone survey of 2,000 adults to learn about the major economic concerns for the future. The survey results showed that 1,740 of the respondents think the future health of Social Security is a major economic concern.

If computing the confidence intervals manually, make sure to use at least three decimal digits for the critical values.

a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern?

b. At 90% confidence, what is the margin of error (to 4 decimals)?

c. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern (to 3 decimals).

(    , ) , ( , )

d. Develop a 95% confidence interval for this population proportion (to 3 decimals).

( , ) , ( , )

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The range for a set of data is estimated to be 24.

e. What is the planning value for the population standard deviation?

f. At 95% confidence, how large a sample would provide a margin of error of 3?

g. At 95% confidence, how large a sample would provide a margin of error of 2?

The number of female customers arriving to a coffee shop follow a Poisson process with a mean rate of 3 per hour. The number of male customers arriving to the same coffee shop also follow a Poisson process with a mean rate of 6 per hour and their arrival is independent of the arrivals of female customers.

a) What is the probability that the next customer will arrive within 5 minutes?

b) What is the probability that exactly thee customers will arrive in the next 5 minutes?

c) What is the probability of exactly two male and exactly one female customer will arrive in the next 5 minutes?

d). Parts b) and c) ask for the probability of exactly three arrivals in the next 5 minutes. Are they identical? Explain why?

e) What is the probability of exactly five customers will arrive between 6 and 7 hours from now?

Suppose a legislator is deciding whether they should put in the effort to draft a bill. The legislator only wants to do this if they are convinced that a majority of their consituents support the bill. The legislator runs a poll of 1,000 constituents, and will be convinced that a majority of their constituents support the bill if the lower bound of the 95% confidence interval for the probability that a constituent supports the bill is greater than 0.50. 550 out of the 1,000 constituents polled indicate support for the bill. Will the legislator put in the effort to draft the bill? (Possible answers are yes or no).

1. An employment information service claims the mean annual pay for full-time workers without a high school diploma is less than $19,100. The annual pay for a random sample of 8 full-time non-high school graduates is listed below. Salaries for people without high school diplomas are normally distributed. Based on this information, you decide to

18,165             16,012             18,803             19,864

17,328             21,445             19,237             18,316

2. A company that makes cola drinks states that the mean caffeine content per one 12-ounce bottle of cola is 35 milligrams. You believe that the mean caffeine content is not 35 milligrams. You decide to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 38.2 milligrams with a standard deviation of 7.5 milligrams.  Based on this information, you decide to

Studies have shown that the frequency with which shoppers browse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you browse online retailers per week?”

1. Use Data > Data Analysis > Correlation to compute the correlation check the Labels checkbox. Show work in excel.

2. Use the excel function =CORREL to compute the correlation. If answer for #1 and 2 do not agree, there is an error. Show work in excel.

A random sample of 30 stocks was selected from each of the three major U.S. exchanges and their performance over the previous year was noted. The median performance for all 90 stocks was noted and the following table constructed, Exchange Median New York 18 American 17 NASDAQ 10 Was there a significant difference in the performance of stocks on the three exchanges during the previous year?

In a recent year the average movie ticket cost $10.50, In a random sample of 50 movie tickets from various areas

What is the probability that the mean cost exceeds $8.50, given that the population standard deviation is $1.50?

True or false: The Markov Analysis is a type of analysis that allows us to predict the future by using the state probabilities and a Matrix of Transition Probabilities.

Use the R script to answer the following questions: (write down your answers in the R script with ##)

(1). Import FarmSize.csv to Rstudio. Use the correct function to build a linear regression model predicting the average size of a farm by the number of farms; Give the model a name (e.g. FarmSize_Model). Call the model name to inspect the intercept and slope of the regression model. Verify the answers in your manual calculation.

(2). Use the correct function to generate the residuals for the 12 examples in the dataset from the model. Create a residual plot, with x axis as independent variable and y axis as residual.

(3). Use the correct function to inspect SSE, Se and r². Write down the values for these measures. Verify the answers in your manual calculation.

(4). Use the correct function to inspect slope statistic testing result. What is the t value for the slope statistic testing? What is the p value? What is the statistical decision?

I need a regression analysis done on the following numbers.

A systematic random sample was taken from the set of all Presidents of the United States. The data file potus heights.csv random sample includes the height (in inches) of each sampled President. (a) From this data, estimate the average height of United States Presidents. Calculate two error bounds for your estimate, one using the usual SRS formula, and one using the successive difference variance estimator. (b) Which variance estimator is more appropriate for these data? Briefly explain

A regional transit company wants to determine whether there is a relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the following data:

Instructions:

1. Input the data into an SPSS work sheet making sure that all your variables are labelled appropriately
2. Create a scatter plot for these data.
3. What does the scatter plot indicate about the relationship between the age of a bus and its annual maintenance costs?
4. What is the correlation coefficient between the age of a bus and annual maintenance cost?
5. Estimate a regression model that could be used to predict the annual maintenance cost given the age of the bus.
6. What is the equation of the estimated model?
7. Test whether each of the regression parameters β₀ and β₁ is equal to zero at the 0.05 level of significance testing.
8. What is the correct interpretations of these parameters?
9. How much of the variation in the sample values of annual maintenance costs does the regression model you estimated explain?
10. What do you predict the annual maintenance cost to be for a 4.5 year old bus?
11. Save all your commands to a syntax file