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1. Explain the difference between

a. A Population and a Sample

- a. A Population consists of everything. A Sample is a subset of a Population

1. Explain the difference between

b. A Parameter and a Statistic

- b. A Parameter is a characteristic measured for a population. A Statistic is a characteristic measured for a sample.

1. Explain the difference between

c. Descriptive Statistics and Inferential Statistics

c. Descriptive Statistics are merely used to describe some characteristics of a variable in a sample, without regard for the corresponding population parameter values. Inferential Statistics push it one step further: We make an inference (i.e., a generalization; an assumption) that the population parameter values are probably close to the corresponding sample statistic values.

1. Explain the difference between

d. A Variable of Interest and a Control Variable

- d. A Variable of Interest is just what it sounds like it is: A variable that we are interested in studying and analyzing in our current work. A Control Variable is a variable that we have data for, but we are not interested in studying or analyzing in our current work.

2. Suppose you measure a nation’s GNP each quarter for thirty years. Is this an example of a “Cross Sectional” or a “Time Series” data set? Why?

Time Series, since the data are collected across different points in time. One possible thing we can study is how these values have changed across time.

3. Suppose you measure the GNP for 87 countries for the third quarter of 2020. Is this an example of a “Cross Sectional” or a “Time Series” data set? Why?

Cross Sectional, since the data are collected at a single point of time and can be analyzed relative to each country, but not across different time periods.

4. A subscription website catering to people who are business executives conducted a marketing survey and asked the following five questions. Classify each resulting variable as either “Categorical (Qualitative)” or “Quantitative,” and briefly explain why.

a. How many nights did you stay in a hotel the past twelve months?

a. Quantitative. The data is counts of counting or measuring how many nights the person stayed in a hotel.

4. A subscription website catering to people who are business executives conducted a marketing survey and asked the following five questions. Classify each resulting variable as either “Categorical (Qualitative)” or “Quantitative,” and briefly explain why.

b. Where do you purchase books: In a Bookstore, On-Line, or from a Book Club?

b. Categorical. The data consist of one of three category labels.

4. A subscription website catering to people who are business executives conducted a marketing survey and asked the following five questions. Classify each resulting variable as either “Categorical (Qualitative)” or “Quantitative,” and briefly explain why.

c. Do you use a travel agent to make your travel arrangements? Write “1” if Yes and “2” if No.

c. Categorical. The data consist of one of three category labels (“1” or “2”)

d. What is your age?

d. Quantitative. The data measures how old a person is (or, counts how many years they have lived).

4. . A subscription website catering to people who are business executives conducted a marketing survey and asked the following five questions. Classify each resulting variable as either “Categorical (Qualitative)” or “Quantitative,” and briefly explain why.

e. How do you generally fly — Private, First Class, Business Class, Economy-Plus, or Economy?

e. Categorical. The data consist of one of five category labels.

c. Do you use a travel agent to make your travel arrangements? Write “1” if Yes and “2” if No.

Suppose that out of a total of 430 respondents, 155 of them answered “1” in part “c” above.

f. Develop a statistic that can be used to estimate the percentage of all business travelers who use a travel agent to make their travel arrangements

f. 155 / 430 = 0.36 . Based upon our sample we infer that 36% of all business travelers use a travel agent.

e. How do you generally fly — Private, First Class, Business Class, Economy-Plus, or Economy?

Suppose that out of a total of 430 respondents, 155 of them answered “1” in part “c” above.

g. If 44% of the 430 respondents said they generally fly Business Class, then how many of the respondents gave that answer in part “e”?

g. (430)(0.44) = 189.2 . So approximately 189 or 190 of the respondent generally fly Business Class.

6. In a sample of 50 businesses in Liechtenstein, ten had between 10 and 19 employees; fourteen had between 20 and 29 employees; seventeen had between 30 and 39 employees; seven had between 40 and 49 employees; and two had between 50 and 59 employees.

a. Construct a Frequency Table for this data. Include columns for Frequency, Relative Frequency, Cumulative Frequency, and Cumulative Relative Frequency.

8. The following scatterplot contains twenty observations for two generic variables, “x” and “y”.

Based on this scatterplot, would you classify the relationship between x any y as being Positive, or Negative, or Null? Why?

There is a Negative relationship between “x” and “y”. Clearly “y” tends to decrease as “x” increases (that is, the two variables tend to move in opposite directions). Note: In this scatterplot I changed the value at which the horizontal axis and the vertical axis cross (i.e., the graph’s origin; it is not the “usual” x=0 and y=0), the minimum and maximum values of each axis, and the size of the gaps between tic marks on each axis. Sometimes you see that in real-world applications ... which is why I did it here!

9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:

a. Mean

a. Using the AVERAGE command in Excel (as per the lecture), we find the mean to be 160. On average, a family in our sample paid $160.00 to have their income taxes prepared.

9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:

b. Median

b. Using the MEDIAN command in Excel (as per the lecture), we find the median to be 135. One-half of the families paid less than $135, and the other half paid more than $135, to have their taxes prepared.

9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:

c. Mode

c. Using the MODE command in Excel (as per the lecture), we find the mode to be 120. The most common amount a family in our sample paid to have their taxes prepared is $120.

d. First Quartile

d. Using the QUARTILE command in Excel (as per the lecture), we find the first quartile (Q1) value to be 115. One-quarter (25%) of the families in our sample paid $115 or less to have their taxes prepared.

e. Third Quartile

e. Using the QUARTILE command in Excel (as per the lecture), we find the third quartile (Q3) value to be 183.75. Three-quarters (75%) of the families in our sample paid $183.75 or less to have their taxes prepared.

f. 90 Percentile

f. Using the PERCENTILE command in Excel (as per the lecture), we find the 90th Percentile (P90) value to be 237. 90% of the families in our sample paid $237 or less to have their taxes prepared.

g. Five-Number Summary

g. Using the MIN and MAX commands in Excel, we find the lowest value is 100 and the highest value is 360. So the Five Number Summary is: 100, 115, 135, 183.75, 360

11. The cost of renting a car for one month in Switzerland varies depending on location and the type of car being rented. Suppose this cost has a mean of 3,100 CHF and a standard deviation of 1,200 CHF. Calculate the standardized value for each of the following costs. Then interpret each of these Z-score values. Finally, explain why each value either would or would not be considered an outlier here.

a. 2,300 CHF

b. 4,900 CHF

c. 13,000 CHF

b. Examining the graph in part “a” we see that there appears to be a positive linear relationship. (The variables tend to move in the same direction; e.g., as one goes up, the other also tends to go up.)

c. Using the CORREL command in Excel (as per the lecture), we find the correlation value to be 0.69.