Explain in your own words, What you know about the central limit theorem. What does it do? When can you use it?

In your own words, Differentiate the following statistical terminology with some examples.

a. Population parameter and Sample Statistic.

b. Descriptive Statistic and inferential Statistic.

C. Nominal Scale and Ordinal Scale

d. Primary Data Source and Secondary Data Sources.

2. Data showing the population by state in million of people follow ( The World Almanac, 2012) The dataset in Excel file 2012Population.XLsx.

a. Develop a frequency distribution, a percent frequency distribution, and a histogram Use a class width of 2.5 million.

b. Does there appear to be any skewness in the distribution? Explain

c. What observation can you nake about the population of the 50 states?

Your neighbor has planted a bed of pink snapdragons in his yard. As the growing season progresses, he notices that some white and red snapdragons are popping up in what was supposed to be a bed of pink flowers. Explain to him the reason that this is happening.

Georgia state. Does your state have an income tax? What percentage of your income do you have to pay in state income tax? What about property taxes and sales taxes? How do these taxes in your area compare to those in three other states and communities of your choice?

Returning to our running case for Shannon’s Brewery introduced in the market share exercise, assume that Shannon’s is considering the introduction of a new craft beer called Irish Stout that will be derived from its award winning Irish Red. Initially, Irish Stout will only be sold “on premise” at the brewery. Currently, pints of Irish Red consumed on premise sell for $5.00 per pint with unit variable costs of approximately $2.75 per pint. Variable costs are predominantly comprised of the costs of ingredients and utilities that directly affect the brewing process. The new craft beer will be positioned at a slightly higher price, $5.25 per pint and its unit variable costs will be about $3.25 due to the higher cost of some ingredients. The relevant price, cost, and margin data are below.

1.) Shannon’s Irish Red averages on premise sales of 1,200 pints per month. What is the anticipated profit (contribution dollars) per month associated with sales of Shannon’s Irish Red assuming that the Irish Stout is not introduced. Express your answer to the nearest dollar. Do not include the dollar sign.

2.) Assume that Shannon’s estimates that the sales of the new Irish Stout will be about 250 pints per month, but 27% of these sales will be cannibalized from sales of Shannon’s Irish Red. Compute the total combined increase (incremental increase or change) in contribution dollars for both Irish Red and Irish Stout expected with cannibalization . Express your answer to the nearest dollar. Do not include the dollar sign.

3.) Let’s stretch a little on this one. Assume Shannon’s Irish Red sells 1,000 pints per month in the absence of any cannibalization. Assume also that the new Irish Stout will sell 500 pints per month. The relevant price and cost data are:

One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroit Red Wings was obtained. The weight (in pounds) of each player was carefully measured, and the resulting data have a sample size of 18 with a sample mean of 205 pounds and a sample standard deviation of 11.6 pounds. You can assume that all of the assumptions are met.

a) What are the assumptions that are required to perform inference on this data?

b) Should you use a z distribution or a t distribution in this problem. Note that you will only get one try to get this question correct.Please explain the correct answer.

c) Find the 98.9% confidence interval for the true mean weight of the players from the Detroit Red Wings. Just answer, no need solution.

c) i) If this would be a z distribution, what would be the critical value? Please use 4 decimal places.

c) ii)  If this would be a t distribution, what would be the critical value? Please use 4 decimal places.

c) iii) If this would be a t distribution, what would be the degrees of freedom?

c) iv) The 98.9% confidence interval for the true mean weight of the players from the Detroit Red Wings is

( , )

2. A public polling agency conducts a survey to determine the current consumer sentiment concerning the state of the economy. Last year's poll shows that 30% of consumers are optimistic about the state of the economy. Suppose the public polling agency randomly samples 485 consumers and finds that only 158 are optimistic about the state of the economy.

a) What is the parameter of interest? explain

b) Construct a 95% confidence interval for the parameter of interest and interpret the confidence intervals.

c) Set up the null and alternative hypotheses for testing whether the current consumer sentiment concerning the state of the economy is different from the last year. (α = 0.05)

d) Sketch a graph and mark the rejection region.

e) Calculate the test statistic value.

f) Make the decision according to the rejection region approach.

g) Give the conclusion base on your decision

use the construction of The circumcircle to construct Euler's line. Describle your construction in detail