How do you interpret the price indices in Exhibit 3? How do economists construct them? Use Excel regression to analyze the relationship between the adjusted price index (dependent variable and year (independent variable). Interpret your regression findings by discussing the coefficient of determination (R-squared), the regression coefficient, the regression equation, and the p value.   Can you use the regression equation to predict the price indices? Take into account statistical, macroeconomic, and other considerations.

EXHIBIT 3

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 2%?

A. 2401

B. 25

C. 1692

D. 4802

What is the difference between a parameter and a statistic? Describe an example. Finally, there are “adjustments” that statisticians make to statistics to make them better represent the parameter, discuss what this looks like with the standard deviation.

Use R to answer the following questions.

Assume that you are interested in testing H0 : E(X) = 20 versus H1 : E(X) 1 20 with a significance level of 5% using the t-test. Let the sample average be equal to 22.7 (?̅ = 22.7) and the sample standard deviation be equal to 5.4 (s = 5.4). The sample size is 55 (n = 55).

1. Do you reject the null hypothesis?

2. If a significance level of 1% is used, do you reject the null hypothesis?

3. If the testing hypotheses are changed to H0 : E(X) = 24 versus H1 : E(X) 1 24 (with a significance level of 5%), do you reject the null hypothesis?

Once you have the answers in R, copy the text commands and results and paste them in a word processor file (e.g., Microsoft Word)

Two students take the same test which consists of 5 questions, each one with 5 answers, each one with only 1 correct answer. If the students respond the test randomly

i) What is the probability that both of the students get the same number of correct answers?

ii) Find the probability that both tests are the same (assume that each test is independent from each other)

iii) What is the expected number of correct answers for each student?

iv) What is the probability that both students pass the test if they have to get at least 3 correct answers to pass it?

A study of depression and exercise was conducted. A total of 5 groups were used: each group differs by the extent to which group members exercise. A depression rating (scale: 1-100, a continuous variable) was given to all 1410 participants in the sample. An incompleted ANOVA table is provided below. What is the obtained F (i.e., value in Cell [8])?

Consider a model in which M balls are distributed between two bins, and at each time point one of the balls is chosen at random and is then removed from its bin and placed in the other one. Let Xn denote the number of balls in bin 1 after the nth switch and let m_n = E[Xn].

(a) Classify all the states of this chain as recurrent or transient (justify your answer!)

(b) Find E[X2|X0 = 2]

Using a BA example, provide an explanation as to why correlation does not equal causation.

Membership selection. A town council has 11 ​members, 6 Democrats and 5 Republicans.

Question 12

A company manufactures 2 types of products P1 and P2. Let X1 and X2 be their respective number of units to be produced each month.

The company has a contract with one of its customers to produce a minimum of 300 units of each product per month. This information can be expressed in the LP as follows

A) Maximize X1 + X2

B) X1+X2 ≥ 600

C) X1+X2 ≥ 300

D) X1 ≥ 300, X2 ≥ 300

When flights are delayed, do two of the worst airports experience delays of the same length? Suppose the delay times in minutes for seven recent, randomly selected delayed flights departing from each of these airports are as follows.

Use the MWW test to determine if there is a difference in length of flight delays for these two airports. Use α = 0.05.

State the null and alternative hypotheses.

H₀: The two populations of flight delays are identical.
H_a: The two populations of flight delays are not identical.H₀: The two populations of flight delays are not identical.
H_a: The two populations of flight delays are identical.    H₀: Median delay time for airport 1 − Median delay time for airport 2 ≤ 0
H_a: Median delay time for airport 1 − Median delay time for airport 2 > 0H₀: Median delay time for airport 1 − Median delay time for airport 2 < 0
H_a: Median delay time for airport 1 − Median delay time for airport 2 = 0H₀: Median delay time for airport 1 − Median delay time for airport 2 ≥ 0
H_a: Median delay time for airport 1 − Median delay time for airport 2 < 0

Find the value of the test statistic.

W =

What is the p-value? (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.    Reject H₀. There is not sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.

The population mean income of US residents is $50,000 with a standard deviation of $20,000. Suppose that we sample 300 US residents and calculate the sample mean.

a) What distribution does the sample mean follow? WHY? Write using proper notation.

b) Find the probability that the mean of our sample is less than $49,000

c) Suppose we sample 3,000 US residents instead. Find the probability that the mean of the sample is less than $49,000. Explain why this probability is smaller.

What is an example in society about Hypothesis testing?

Consider a population proportion p = 0.20. [You may find it useful to reference the z table.]

a. Calculate the standard error for the sampling distribution of the sample proportion when n = 20 and n = 58? (Round your final answer to 4 decimal places.)

20=0.0894

58= 0.0525

b. Is the sampling distribution of the sample proportion approximately normal with n = 20 and n = 58?

c. Calculate the probability that the sample proportion is between 0.18 and 0.20 for n = 58. (Round "z-value" to 2 decimal places and final answers to 4 decimal places.)

A study was perform in the Albuquerque, New Mexico metropolitan area to evaluate the diagnostic accuracy of Prostate Specific Antigen (PSA) testing as a screening tool for detecting prostate cancer in community practice. Subjects were 2,620 men 40 years and older undergoing (PSA) testing and prostate biopsy. A total of 1,932 men tested positive with the initial PSA testing and among them cancer was detected in 800 subjects with a subsequent prostate biopsy. In addition, 130 cases of prostate cancer were detected among men who screened negative with the initial PSA test.

a) Using the information above, create a 2x2 table to assess the accuracy of the test.

b) Calculate and interpret the sensitivity of the PSA test.

c) What will be the specificity of this screening test? Calculate and interpret.

d) Calculate and interpret the predictive value positive of the PSA test.

e) Calculate and interpret the predictive value negative of the PSA test