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.

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:

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ? 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 10.410.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 510 .

In answering the questions, use ?‑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 505 and 515? (Enter your answer rounded to four decimal places.)

Probability - ?

(b) You sample 2525 students. What is the standard deviation of the sampling distribution of their average score ?¯  ? (Enter your answer rounded to two decimal places.)

Standard Deviation - ?

(c) What is the probability that the mean score of your sample is between 505505 and 515515 ? (Enter your answer rounded to four decimal places.)

Probability - ?

Some studies have shown that in the United States, men spend more than women on Valentine's Day. A researcher wants to estimate how much more men spend by observing the amounts spent for random samples of men and women. We want to estimate the difference (µ _men - µ _women) using a 90% confidence interval.

a) Find the AD (Anderson-Darling) for both Men and Women (using Minitab). (round to 3 decimal places)

b) Report the endpoints of the 90% confidence interval below. (Round to 1 decimal place)

MNO, Inc., a publicly traded manufacturing firm in the United States, has provided the following financial information in its application for a loan. The market value of equity is 1.58 times the book value of debt. Retained earnings are 5.27% of total assets. Sales are 52% of total assets. Earnings before interest and taxes are 32.87% of total assets. Finally, Working capital is 34.25% of total assets.

a) What is the Altman discriminant function value for MNO, Inc.?

b) Should you approve MNO, Inc.'s application to your bank for a $5,000,000 capital expansion loan?

c) If sales for MNO were 38% of total assets and the market value of equity was only half of book value, would your credit decision change?