Sales of roof material, by quarter, since 2005 for Carolina Home Construction Inc. are shown below (in $ thousands).

1. Determine the typical seasonal patterns for sales using the ratio-to-moving-average method. (PLEASE DONOT USE EXCEL. PLEASE SHOW ALL MANUAL WORKINGS HOW DID YOU GET ANSWER IN THE TABLE)

2. Deseasonalize the data and determine the trend equation. PLEASE DONOT USE EXCEL. PLEASE SHOW ALL MANUAL WORKINGS HOW DID YOU GET ANSWER IN THE TABLE)

3. Project the sales for 2012, and then seasonally adjust each quarter.

A ski company in Vail owns two ski shops, one on the west side and one on the east side of Vail. Ski hat sales data (in dollars) for a random sample of 5 Saturdays during the 2004 season showed the following results. Is there a significant difference in sales dollars of hats between the west side and east side stores at the 10 percent level of significance?

(b) State the decision rule for a 5 percent level of significance. (Round your answers to 3 decimal places.)

Reject the null hypothesis if t_calc < ( ) or t_calc > ( ).

(c-1) Find the test statistic t_calc. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.)

t_calc ( )

Have you ever noticed that, when you tear a fingernail, it tends to tear to the side and not down into the finger? (Actually, the latter doesn’t bear too much thinking about.). Why might this be so? One possibility is that fingernails are tougher in one direction than another. A study of the toughness of human fingernails compared the toughness of nails along a transverse dimension (side to side) compared with a longitudinal direction, with 15 measurements of each (Farren et al., 2004). The toughness of fingernails along a transerve direction averaged 3.3 kJ/m2, with a standard deviation of 0.95, while the mean toughness along the longitudinal direction was 6.2 kJ/m2, with a standard deviation of 1.48 kJ/m2. a) Test for a significant difference in the toughness of these fingernails along two dimensions. b) As it turns out, all of the fingernails in this study came from the same volunteer. Discuss what the conclusion in part (a) means. What would be required to describe the fingernail toughness of all humans?

1. The annual precipitation measurements (Pi in cm) for M city, over a 20year period are shown in the following table. Determine the mean, standard deviation, and skew coefficient for this series.

2. Annual precipitation measurements (Pi in cm) for M City, were given in Problem 1. Determine the magnitude of the 10-year precipitation depth if the data fit:

1. the normal distribution.
2. the Gumbel distribution.

How many times was the P10 (normal) exceeded in the 20-year annual precipitation record given in Problem 1 ?

Please clarify each step of the solution

1. The annual precipitation measurements (Pi in cm) for M city, over a 20year period are shown in the following table. Determine the mean, standard deviation, and skew coefficient for this series.

2. Annual precipitation measurements (Pi in cm) for M City, were given in Problem 1. Determine the magnitude of the 10-year precipitation depth if the data fit:

1. the normal distribution.
2. the Gumbel distribution.

How many times was the P10 (normal) exceeded in the 20-year annual precipitation record given in Problem 1 ?

Please clarify each step of the solution

1. The annual precipitation measurements (Pi in cm) for M city, over a 20year period are shown in the following table. Determine the mean, standard deviation, and skew coefficient for this series.

2. Annual precipitation measurements (Pi in cm) for M City, were given in Problem 1. Determine the magnitude of the 10-year precipitation depth if the data fit:

1. the normal distribution.
2. the Gumbel distribution.

How many times was the P10 (normal) exceeded in the 20-year annual precipitation record given in Problem 1 ?

Please clarify each step of the solution

High-School Confidential

Notes on Teen Movies

David DENBY

More info:

David Denby (b. 1943), who lives in New York City, is a staff writer and film critic for the New Yorker and the former film critic for New York. His writing has also appeared in the Atlantic, the New York Review of Books, and the New Republic. His first book, Great Books: My Adventures with Homer, Rousseau, Woolf, and Other Indestructible Writers of the Western World (1996), was a finalist for the National Book Critics Circle Award. Denby is also the editor of Awake in the Dark: An Anthology of Film Criticism from 1915 to the Present (1977), American Sucker (2004), and Snark (2009). The essay that follows was originally published in the New Yorker in May 1999.

What is Denby's opinion of teen movies? Does he find anything redeeming in them?

Use quotes from the reading to support your ideas.

The article “Determination of Carboxyhemoglobin Levels and Health Effects on Officers Working at the Istanbul Bosphorus Bridge” (G. Kocasoy and H. Yalin, Journal of Environmental Science and Health, 2004:1129–1139) presents assessments of health outcomes of people working in an environment with high levels of carbon monoxide (CO). Following are the numbers of workers reporting various symptoms, categorized by work shift. The numbers were read from a graph.

Can you conclude that the proportions of workers with the various symptoms differ among the shifts?

(a) State the appropriate null hypothesis.

(b) Compute the expected values under the null hypothesis.

(c) Compute the value of the chi-square statistic.

(d) Find the p-value. What do you conclude?

Stocks A and B have the following historical returns:

(a) Calculate the average rate of return and standard deviation of returns (as percents) for each stock during the 5-year period. (Round your standard deviations to two decimal places.)

stock A average rate of return %

standard deviation %

stock B average rate of return %

standard deviation %

(b) Assume that someone held a portfolio consisting of 50% of stock A and 50% of stock B and that the average annual realized returns and past volatility of each stock are unbiased estimators of their expected returns and future volatility. What is the portfolio's expected return and the volatility of next year's returns (as percents)? The correlation between the returns of the two stock is 90.83%. (Round your answers to two decimal places.)

expected return %

volatility %

Part 2: t-Procedures

In this part, we will use t-procedures. t-procedures are both confidence intervals and hypothesis tests that

use a t distribution. They are called t-procedures because they rely on a t-test statistic and/or a t-critical

value, so we only need to know the results of a sample in order to perform these procedures for a population

mean.

In Part 2, you will use the data file TempSample00-18.

(THIS IS THE DATA)

YEAR,Month,High Temperature

2000,Jan,45

2000,Jan,48

2001,Jan,49

2003,Jan,62

2003,Jan,53

2004,Jan,42

2004,Jan,47

2005,Jan,40

2005,Jan,47

2006,Jan,48

2006,Jan,47

2007,Jan,51

2007,Jan,34

2007,Jan,47

2009,Jan,50

2011,Jan,35

2012,Jan,44

2013,Jan,38

2013,Jan,53

2013,Jan,42

2014,Jan,58

2014,Jan,47

2014,Jan,44

2015,Jan,52

2016,Jan,44

2017,Jan,49

2018,Jan,54

2000,Feb,48

2001,Feb,47

2004,Feb,47

2007,Feb,51

2008,Feb,51

2008,Feb,55

2011,Feb,45

2014,Feb,37

2014,Feb,54

2014,Feb,58

2015,Feb,54

2017,Feb,52

2017,Feb,44

2017,Feb,45

This includes an SRS of daily temperature highs from January and February from the years 2000-2018

(i.e. "recent" highs). The distribution of "recent" daily high temperatures is approximately Normal.

2.1 Getting Started

2.1.1 Understanding the Set-Up

1) Describe the intended population?

2) Describe the sample?

3) Describe the variable of interest?

4) Describe the parameter of interest (in context)?

5) Describe the statistic of interest (in context)? Give a numerical value along with your description.

Round to two decimal places.

2.1.2 Checking Conditions

1) Check that the conditions for using t-procedures are satisfied. If they are not, discuss whether or not it is reasonable to use t-procedures.

2.2 Confidence Intervals

2.2.1 Motivating Question: Confidence Intervals

In 2.2, we will try to answer the question:

What is the average daily temperature high in Portland, OR for the

months of January and February during 2000-2018?

2.2.2 Confidence Interval

1) What degrees of freedom are needed?

2) What critical value is used to compute a 95% confidence interval?

3) Give the 95% confidence interval. Round to two decimal places.

4) Interpret your 95% confidence interval.

2.2.3 Wrap Up

1) Answer the motivating question in 2.2.1.

2.3 Hypothesis Tests (Tests of Significance)

2.3.1 Motivating Question: Hypothesis Tests

In 2.3, we will try to answer the question:

Is there evidence to suggest that the average daily temperature high in Portland,

OR for the months of January and February during 2000-2018 is different than

the historical average of 48.35◦F?

2.3.2 Hypothesis Test

1) Perform a hypothesis test for α = .01. Be sure to interpret your p-value in context.

2.3.3 Wrap Up

1) Answer the the motivating question in 2.3.1.

2.4 Final Remarks

1) Based on the data found in Part 2, what would you say about the daily high temperature for "recent"

years compared to "historical" years?