In the US I want to know what proportion of 13-year-olds vape. Three distributions are associated with this question: population distribution, sample distribution, and sampling distribution. Describe the role of each in answering this question.

In cross-sectional analysis explain why it is necessary to take a random sample.

Describe the difference between an estimator and an estimate and explain why estimators are random variables while estimates are not.

Explain why point estimates are always wrong.

Discuss the applications of ANOVA (One-Way ANOVA, Two-Way ANOVA) and regression techniques in the context of e-commerce firms like Amazon, Flipkart etc.

Let X and Z be two independently distributed standard normal random variables and let Y=X2+Z.

iShow thatE(Y|X) =X2

iiShow thatμY= 1

iiiShow thatE(XY) = 0ivShow that cov(X,Y) = 0 and thus ρX,Y= 0

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a marketing survey, a random sample of 1010 supermarket shoppers revealed that 266 always stock up on an item when they find that item at a real bargain price.

(a)

Let p represent the proportion of all supermarket shoppers who always stock up on an item when they find a real bargain. Find a point estimate for p. (Enter a number. Round your answer to four decimal places.)

(b)

Find a 95% confidence interval for p. (For each answer, enter a number. Round your answers to three decimal places.)
lower limit     
upper limit     

Give a brief explanation of the meaning of the interval.

5% of all confidence intervals would include the true proportion of shoppers who stock up on bargains

95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.   

5% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

95% of all confidence intervals would include the true proportion of shoppers who stock up on bargains.

(c)

As a news writer, how would you report the survey results on the percentage of supermarket shoppers who stock up on items when they find the item is a real bargain?

Report the margin of error.

Report p̂.  

  Report p̂ along with the margin of error.

Report the confidence interval.

What is the margin of error based on a 95% confidence interval? (Enter a number. Round your answer to three decimal places.)

Two rolls of a fair die. Let x and y be the results of the two rolls, and let z = x + y.

(a) Find P[x = 4, y = 3], P[x > 3, y = 5].

(b) Find P[z = 7], P[z = 5], P[z = 3].

(c) Find the probability that at least one 6 appears given that z = 8.

(d) Find the probability that x = 6 given that z > 8.

(e) Find the probability that z = 7 given that at least one 4 was rolled. (f) Find the probability that z > 7 given that y = 4.

What is the level measurement of the following Operational Definitions. i.e., Nominal, Ordinal or Interval level data?

1 The unemployment rates of the 50 states.

2 The region of country in which people were born

3 How frequently people attended religious services in the last two months.

4 The number of employees in different government agencies.

5 The number of times incumbent senators voted the way the president wanted them to vote on key pieces of legislation.

6 The occupation of candidates for public office (i.e. educator, lawyer, farmer, business person).

7 The percent of different corporations’ pretax profit accounted for by overseas sales.

8 Whether people read the daily newspaper every day, almost every day, frequently, occasionally, seldom, or never.

Gregor Mendel established the concept of dominant and recessive genes and characteristics. According to Mendel’s law when crossing two inbred lines, 75% of the offspring should show dominant and 25% recessive characteristics. In his 19th century work studying inheritance of seed form in peas, Mendel observed 7,324 individuals, 5,474 of which had dominant characteristics.

a. Does this support or contradict Mendel’s law? Explain.

b. If the observation would be 5,566 (out of 7,324), would it be likely that his conjecture is true, i.e., 75% percent would show dominant characteristics? Explain.

Allele frequency is the relative frequency of a certain allele type among a certain population. Suppose that within a certain area, the allele frequency of A, B and O are 0.2, 0.1, and 0.7, respectively. Suppose that when randomly picking up a person, the first allele type is independent of the second allele type regardless of the type. Calculate the following probabilities:

• The probability for this person to have type O blood.

• The probability for this person to have type A blood.

• The probability for this person to have type B blood.

• The probability for this person to have type AB blood.

When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 42 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 3000 3000 ​batteries, and 3​% of them do not meet specifications. What is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

A survey reported that 37% of people plan to spend more on eating out after they retire. If

eight people are randomly​ selected, determine the values below.

Consider the quarterly electricity production for years 1-4: Year 1 2 3 4 Q1 99 120 139 160 Q2 88 108 127 148 Q3 93 111 131 150 Q4 111 130 152 170 (a) Estimate the trend using a centered moving average. (b) Using a classical additive decomposition, calculate the seasonal component. (c) Explain how you handled the end points. Note: Explain all the steps and computations in your own words and it should be typed on Microsoft word .

Locate the results of a recent survey that show at least two variables in a newspaper, magazine, or internet article. Outline the survey data so that your peers can understand the variables and results. Then identify at least one key statistical inference formula involving two of more parameters that you could use to evaluate the data. Provide a brief explanation of why you selected the formula you did and why it matters. Also, explain what the formula is and where it is in the textbook and clearly define your parameters. Do not use regression or correlation examples since we will cover them during the next module.

Be sure to support your statements with logic and argument, citing any sources referenced.

As a shift manager at a local fast food place, you are responsible for ensuring quality control. You do not want to weigh all the frozen hamburger patties that get delivered by your supplier to make sure they weigh four ounces on average, so you choose 25 patties at random. You calculate that the sample mean weight of patties is 3.4 ounces and the standard deviation of the weight of hamburger patties to be 0.5 ounces.

(a) Test the hypothesis that the population mean weight of patties is equal to 4 ounces.

(b) You are particularly concerned about the population weight being under 4 ounces, is there any reason for concern? Explain using the concept of a confidence interval.

What is the difference between a Paired t-test and a Pooled t-test?