In the united states, paper currency often comes into contact with cocaine directly, during drug deals or usage, or in counting machines where it wears off from one bill to another. A forensic survey collected fifty $1 bills and measured the cocaine content of the bills. Forty-six of the bills had measurable amounts of cocaine on them. Assume that the sample of bills was a random sample. Please answer the following questions.

1. (a) Suppose that the US Treasury Department claims that 4 out of 5 circulating American 1$ bills contain residues of cocaine. Is there any evidence based on these results that the claim is incorrect? Note: find the p-value using pbinomor dbinom.

2. (b) For the test in (a), is there evidence of incorrectness at level 0.01? Explain, briefly.

3. (c) What sort of error could you be making in (a)? Explain briefly, in the context of the problem.

The Cheesecake Factory Incorporated​ (NASDAQ: CAKE​) operates two bakeries in the United States where it makes over 70 desserts for its own restaurants. In​ addition, the Cheesecake Factory bakeries sell selected desserts to a variety of foodservice operators and​ retailers, including Sam's Club​, Walmart​, Target​, BJ's Wholesale Club​, and Barnes & Noble Cafés. The Cheesecake Factory has accounts receivable on its financial statements. The primary source of its accounts receivable is its sales to bakery customers.

** There is no financial statement to reference**

1. When The Cheesecake Factory ships an order to BJ's Wholesale Club on​ account, The Cheesecake Factory​'s total assets would​ (ignore the cost of sales journal entry for this​ question):

a. increase

b. stay the same

c. decrease

d. unable to determine with the information provided

2. When The Cheesecake Factory ships an order to BJ's Wholesale Club on​ account, The Cheesecake Factory​'s total liabilities would​ (ignore the cost of sales journal entry for this​ question):

a. increase

b. stay the same

c. decrease

d. unable to determine with the information provided

3. When The Cheesecake Factory ships an order to BJ's Wholesale Club on​ account, The Cheesecake Factory​'s total equity would​ (ignore the cost of sales journal entry for this​ question):

a. increase

b. stay the same

c. decrease

d. unable to determine with the information provided

4. When The Cheesecake Factory receives payment for an order it shipped to a wholesale customer last​ month, The Cheesecake Factory​'s total assets​ would:

a. increase

b. stay the same

c. decrease

d. unable to determine with the information provided

Suppose the preliteracy scores of three-year-old students in the United States are normally distributed. Shelia, a preschool teacher, wants to estimate the mean score on preliteracy tests for the population of three-year-olds. She draws a simple random sample of 20 students from her class of three-year-olds and records their preliteracy scores (in points).

80,82,83,85,86,91,91,92,92,93,95,97,99,100,100,103,107,108,111,112

a) Calculate the sample mean, sample standard deviation, and standard error (SE) of the students' scores. Round your answers to four decimal places.
b) Determine the t-critical value (t) and margin of error (m) for a 95% confidence interval. Round your answers to three decimal places.
c) What are the lower and upper limits of a 95% confidence interval? Round your answers to three decimal places.
d) Which is the correct interpretation of the confidence interval:

Shelia is 95% confident that the true population mean is between 91.129 points and 99.571 points.

There is a 95% chance that the true population mean is between 91.129 points and 99.571 points.

Shelia is 95% confident that the true population mean is between 90.842 points and 99.858 points.

There is a 95% chance that the population mean is between 90.842 points and 99.858 points.

Shelia is certain that the true population mean is between 90.842 points and 99.858 points.

Congratulations! You have been appointed an economic policy advisor to the United States. You are told that the economy is significantly below its potential output and that the following will happen next year: World income will fall significantly due to the pandemic, and the price of oil will fall significantly due to lack of economic activities, as well as the availability of alternative and more sustainable energy sources (wind, solar, hydro, nuclear), and the U.S. is an oil exporter, along with shale and natural gas.

a) What kind of policies (under Fiscal policy) might you suggest to the government? Mention three.

b) Consider the economic principle held by Classical economists: The economy always returns to its potential in the long run. What are Keynes’s criticisms of this economic principle?

During the 1950s, both the United States and Soviet government's implemented their own forms of so-called "civil defense," to help their civilian populations respond to the new nuclear threat. Describe the official purpose of these programs, and also address the following questions: 1) Were the civil defense programs actually useful or realistic? Why or why not? 2) If they were not realistic in terms of helping people survive a thermonuclear attack, what purpose did they serve?

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ?μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495495 .

In answering the questions, use ?z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490490 and 500500 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score ?¯x¯ ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490490 and 500500 ? (Enter your answer rounded to four decimal places.)

probability:

Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below.

Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 5% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: ?₁ = ?₂ = ?₃; H₁: At least two means are equal . .H_o: ?₁ = ?₂ = ?₃; H₁: Exactly two means are equal.    H_o: ?₁ = ?₂ = ?₃; H₁: Not all the means are equal.   H_o: ?₁ = ?₂ = ?₃; H₁: All three means are different.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 4 decimal places for MS_BET, and MS_W.)

Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?
(numerator)
(denominator)

(c) Find the P-value of the sample test statistic. (Use 4 decimal places.)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P value is greater than the level of significance at ? = 0.05, we do not reject H₀. Since the P value is less than or equal to the level of significance at ? = 0.05, we reject H₀.    Since the P value is greater than the level of significance at ? = 0.05, we reject H₀. Since the P value is less than or equal to the level of significance at ? = 0.05, we do not reject H₀.

(e) Interpret your conclusion in the context of the application.
At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal. At the 5% level of significance there is sufficient evidence to conclude that the means are all equal.    At the 5% level of significance there is insufficient evidence to conclude that the means are all equal. At the 5% level of significance there is sufficient evidence to conclude that the means are not all equal.

What is your favorite color? A large survey of countries, including the United States,
China, Russia, France, Turkey, Kenya, and others, indicate that most people prefer the color
blue. In fact, about 24% of the population claim blue as their favorite color (Reference: Study by
J. Bunge and A. Freeman-Gallant, Statistics Center, Cornell University). Suppose a random
sample of 56 college students were surveyed and 12 of them said that blue is their favorite
color. Does this information imply that the color preference of all college students is different
from that of the general population? Use 5% level of significance.
a. Identify the underlying distribution and state why.
b. State the null hypothesis.
c. State the alternative hypothesis.
d. Circle one: One Tail Test / Two Tail Test.
e. State the critical value for the hypothesis test.
f. Illustrate graphically the rejection region.
g. Compute the test statistic.
h. Find the p-value for the test statistic.
i. Give the significant statement for the hypothesis test: At the ________ level of significance,
there is ______________________ evidence to reject the null hypothesis.
j. State the critical value for the estimation of the confidence interval.
k. Construct a 95% confidence interval for the true proportion of people who prefer color blue.
i. Margin of error:
ii. Confidence Interval:
l. Give the confidence statement for the confidence interval: I am _________ confident that the
true ____________________ of individuals who prefer color blue is between ____________
and ______________.

What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 59 college students were surveyed and r = 11 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.24; H₁: p ≠ 0.24H₀: p = 0.24; H₁: p < 0.24    H₀: p ≠ 0.24; H₁: p = 0.24H₀: p = 0.24; H₁: p > 0.24

(b) What sampling distribution will you use?

The Student's t, since np < 5 and nq < 5.The standard normal, since np < 5 and nq < 5.    The standard normal, since np > 5 and nq > 5.The Student's t, since np > 5 and nq > 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

1. Petal Providers Corporation opens and operates “mega” floral stores in the United States. The idea behind the superstore concept is to model the U.S. floral industry after its European counterparts, whose flower markets generally have larger selections at lower prices. Revenues were $1 million with net profit of $50,000 last year when the first Petal Providers floral outlet was opened. If the economy grows rapidly next year, Petal Providers expect its sales to grow by 50 percent. However, if the economy exhibits average growth, Petal Providers expects a sales growth of 30 percent. For a slow economic growth scenario, sales are expected to grow next year at a rate of 10 percent. Management estimates the probability of each scenario occurring to be rapid growth (0.30), average growth (0.50), and slow growth (0.20). Petal Providers’ net profit margins are also expected to vary with the level of economic activity next year. If slow growth occurs, the net profit margin is expected to be 5 percent. Net profit margins of 7 and 10 percent are expected for the average-and-rapid-growth scenarios, respectively.
   1. Estimate the average sales growth rate for Petal Providers for next year.
   2. Estimate the dollar amount of sales expected next year under each scenario, as well as the expected value sales amount.
   3. Estimate the dollar amount of net profit expected next year under each scenario, as well as the expected value net profit amount.