Observations of any variable recorded over a sequential period of time are considered time-series. Forecasting models, used to estimate values for some future period, are generally classified as either qualitative or quantitative.

Use the internet to research the differences between a qualitative forecasting model and a quantitative forecasting model.

Assume you are an executive of a large transportation company, and your firm's profit is highly sensitive to fuel cost. The price of gasoline and diesel changes daily, however, your customers expect to be quoted a price for delivery services days, weeks, and sometimes, MONTHS in advance. Therefore, your firm relies heavily on forecasting the price of fuel. Which method of forecasting might you use, qualitative or quantitative? And finally, what are the limitations to business forecasting.

If a die is rolled 300 times, use the Chebyshev inequality to estimate the probability
that the number of occurrences of "three" does not lie strictly between 45 and 55.

We compare the yearly income of a designer in Baguio and Manila, two cities in the Philippines. It is known from experience that the variance of yearly incomes in Baguio is ₱40,000 and the variance for yearly incomes in Manila is ₱90,000. A random sample of 20 families was taken in Baguio, yielding a mean yearly income of ₱47,000, while a random sample of 30 families was taken in Manila, yielding a mean yearly income of ₱52,000. At the alpha= .01 significance level, test whether or not there is a significant different in average yearly income between the two cities.

For each of the following variables, please identify the appropriate level of measurement/ primary scale: nominal, ordinal, interval, ratio

a.   Stock price

2. Socioeconomic status (coded as “low income”, “middle income” and “high income”)
3. Number of days since you last ate in a restaurant (the exact number)
4. Number of days since you last ate in a restaurant coded as (1=Within the past week, 2=With the past 2 weeks, 3=Within the past month, 4=Within the past 3 months, 5=More than 3 months ago)
5. Zip code
6. Share of wallet (%)
7. Favorite sports team (e.g., “Yankees”, “Mets”, “Knicks”, etc.)
8. Likelihood to recommend (on an 11-point scale where 0=Definitely would NOT recommend and 10=Definitely would recommend)
9. Overall satisfaction (on a 7-point scale where -3=Extremely dissatisfied, -2=Dissatisfied, -1=Somewhat dissatisfied, 0=Neutral, 1 = Somewhat satisfied, 2= satisfied, 3=Extremely satisfied)
10. Distance from your home to the nearest gas station (in miles, e.g., 2.4 miles)

A health study tracked a group of persons for five years. At the beginning of the study, 25% were classified as heavy smokers, 35% as light smokers, and 40% as nonsmokers. Results of the study showed that light smokers were twice as likely as nonsmokers to die during the five-year study, but only half as likely as heavy smokers. A randomly selected participant from the study died over the five-year period. Compute the probability that the participant was a nonsmoker.

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you​ survey? Assume that you want to be

9090​%

confident that the sample percentage is within

1.51.5

percentage points of the true population percentage. Complete parts​ (a) and​ (b) below.

a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.

nequals=nothing

​(Round up to the nearest​ integer.)

b. Assume that a prior survey suggests that about

3232​%

of air passengers prefer an aisle seat.

nequals=nothing

​(Round up to the nearest​ integer.)

Refer to the accompanying data set and construct a 90​% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.

Construct a 90​% confidence interval of the mean pulse rate for adult females.

___ bpm < mu < ___ bpm

​(Round to one decimal place as​ needed.)

Construct a 90​% confidence interval of the mean pulse rate for adult males.

___ bpm < mu < ___ bpm (Round to one decimal place as​ needed.)

Compare the results.

A. The confidence intervals do not​ overlap, so it appears that adult females have a significantly higher mean pulse rate than adult males.

B. The confidence intervals​ overlap, so it appears that adult males have a significantly higher mean pulse rate than adult females.

C. The confidence intervals​ overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.

D. The confidence intervals do not​ overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.

Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 229 numbers from this file and r = 87 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1.

(i) Test the claim that p is more than 0.301. Use α = 0.10.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.301; H₁:  p ≠ 0.301H₀: p = 0.301; H₁:  p < 0.301     H₀: p = 0.301; H₁: p > 0.301H₀: p > 0.301; H₁:  p = 0.301

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


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is greater than 0.301.There is insufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is greater than 0.301.     

(ii) If p is in fact larger than 0.301, it would seem there are too many numbers in the file with leading 1's. Could this indicate that the books have been "cooked" by artificially lowering numbers in the file? Comment from the point of view of the Internal Revenue Service. Comment from the perspective of the Federal Bureau of Investigation as it looks for "profit skimming" by unscrupulous employees.

Yes. There seems to be too many entries with a leading digit 1.No. There seems to be too many entries with a leading digit 1.     Yes. There does not seem to be too many entries with a leading digit 1.No. There does not seem to be too many entries with a leading digit 1.

(iii) Comment on the following statement: If we reject the null hypothesis at level of significance α , we have not proved H₀ to be false. We can say that the probability is α that we made a mistake in rejecting H_o. Based on the outcome of the test, would you recommend further investigation before accusing the company of fraud?

We have proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.We have not proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.     We have not proved H₀ to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.We have not proved H₀ to be false. Because our data lead us to accept the null hypothesis, more investigation is not merited.

A sample of men and women were compared with regards to one important question. The question was, “Do you research your dates online before you go out with them?” Thirty-five percent of a sample of 40 men and 48% of a sample of 80 women replied “yes” to this question. Provide a confidence interval estimate for the true difference in proportions between men and women who will research their dates online before they go out with them.    

An average of 12 ounces of beer is used to fill each bottle in a local brewery as recorded. The manager now believes that, in general, beer bottles are overfilled. He takes a random sample of 30 bottles to test. The sample mean weight of the bottles is 12.8 ounces with a standard deviation of 1.5 ounces. Conduct a one-sample t-test to test whether the beer bottles are overfilled. Use 5% level of significance. (Round your steps to 4 decimal places, round the t test statistic to 3 decimal places)

A random sample of 31 ice cream cones from McDonald's was weighted, the sample mean weight was 3.5 ounces with a standard deviation of 0.75 ounces. Construct a 99% confidence interval to estimate the overall mean weight of McDonald's ice cream cones. (Round your intermediate steps to 4 decimal places, and final answer to 2 decimal places) (10 points)

A railway company used 2 types of wheel mounts that differ in the way they handle track irregularities: type A and type B. The following data gives the repair records for 2 types over a 1 year period:

Test for the difference between population proportions P_A and PB.Use α = 0.02.

We are studying the relationship of age in years and height in inches for children of ages from 2 - 10. We have a sample of five children. It is a linear relationship, so please find:

(a) r

(b) r(sq);

(c) the equation of the regression line

(d) the expected height in inches for a 7 year-old child.

The data below shows the time to exhaustion after drinking chocolate milk and time to exhaustion after drinking carbohydrate replacement drink by 6 men in a study of effectiveness of 2 types of drinks. Is there any evidence that the mean time to exhaustion is lesser after chocolate milk? Use α = 0.0025.