Q1)  Is the following an example of a categorical measure or a quantitative measure?

Q2)  Is the following a nominal measure?

Q3)  Is the following an ordinal measure?

Q4)  Is the following an interval measure?

Q5)  In the following scenario, is the net value of the customer's account a ratio measure?

Q6)  Is the following a bimonial variable or a multinomial variable?

Q7)  A histogram is shown above. What is its proper interpretation?

Q8)  A box plot is shown above. It is based on a survey of consumers who evaluated a new product in their home for one week. The rating scale was 1 ("Very negative evaluation") to 12 ("Very positive evaluation"). What is the proper interpretation of the box plot?

Q9)  A scatterplot is shown above. It shows almost two years of data: monthly advertising expenditures (A_E) plotted against monthly unit sales (U_E). What is the proper interpretation of the scatter plot?

TABLE:

Westman Electronics is a supplier of industrial electronic equipment. Last year, they had over $20MM in revenue. They have 192 salespeople, and all the sales were channeled through a salesperson. Westman's VP of Sales and Marketing has a dataset that shows last year's sales (in dollars) for each of the 192 salespeople; she is analyzing this as each salesperson's "sales performance." The table above summarizes the sales performance data. Based on the table, which of the following three statements are true?

Q10)  The average of sales performance among all the firm's salespeople was $107,483.

Q11)  We can conclude from the table that 25% of the salespeople had a sales performance that was greater than $141,368.

Q12)  The median sales performance is lower than the mean sales performance.

Q13)  Bonus question: What does the answer to Q12 suggest for the presence of skew and/or outliers?

Q14)  What is suggested by the skewness value that is shown in the table?

Q15)  What does the standard deviation shown in the table suggest?

Q16)  Bonus question: Why do you suppose that the mode is listed as "--N/A--" on the table?

Q17)  A histogram is shown above. Is this distribution approximately uniform, normal, or binomial?

Q18)  In inferential statistics, the researcher is interested in some "population," and taking a "sample" is a technique for making inferences about the "population."

Q19)  In inferential statistics, the only way to be 100% certain about the population is to use proper sampling methods and statistical calculations. Any violation of these methods or assumptions will reduce the certainty away from the 100% level.

Q20)  Unfortunately, if a population is very large, any inferences we make about the population are very uncertain. Even if we have a sample that is representative of the population, the sheer size of the population means that the truth is unknowable (at least unknowable in terms of inferential statistics).

Q21)  Sampling error should give managers uncertainty about inferences that are based on measures from a sample rather than measures from the entire population.

Q22)  The greater the standard error, the greater our uncertainty due to sampling error.

Q23)  The greater the standard error, the greater the margin of error.

Q24)  The smaller the standard error, the more narrow the confidence interval (i.e., the smaller the difference between the lower bound and the upper bound of the confidence interval).

Q1)  Quantitative measure

Q2)  No, it is not a nominal measure       ⇽ Actually, it's an ordinal measure.

Q3)  No, it is not an ordinal measure       ⇽ Actually, it's a nominal measure.

Q4)  No, it is not an interval measure       ⇽ Because the intervals in the underlying construct between one category and the next are not consistent for all categories.

Q5)  Yes, it is a ratio measure       ⇽ Because dollars represent equal intervals on the scale and the zero-point on the scale has a substantive meaning (i.e., "no value").

Q6)  It is a binomial variable       ⇽ Because there are only two possible values

Q7)  All the above

Q8)  Positive (i.e., supportive of the product)       ⇽ Although the box plot indicates that some people gave a very low evaluation, it indicates that 75% of the participants gave it a 9 or higher. Overall, that's a positive evaluation.

Q9)  None of the above

Q10)  True

Q11)  True       ⇽ This is based on the definition of the 3rd Quartile.

Q12)  True

Q13)  Bonus question: It suggests there is a long tail (or a few extreme outliers) on the positive side of the scale       ⇽ The mean is more sensitive to skew and outliers than the median. When the mean is higher than the median, that typically indicates the mean is being drawn higher by positive skew and/or outliers.

Q14)  There is a long "tail" of salespeople who are doing better than the rest, with a few of them performing especially well.       ⇽ In case it's helpful, I've put the histogram of the sales data at the bottom of this page.

Q15)  Performance was very dissimilar among all salespeople. Some of them are performing much better than the average, and some of them are performing much worse than the average.

Q16)  Bonus question: All of the sales performance values happen to be unique (i.e., there are no duplicates), so there is no mode in the data. Or, if you prefer, all the values are the mode. Either way, mode is not meaningful for these data.

Q17)  Normal

Q18)  True

Q19)  False       ⇽ In inferential statistics, we can never be 100% confident of our results. Sampling error is an inherent part of inferential statistics. The only way to be 100% confident is to measure the entire population, and that's not inferential statistics. This isn't mere wordplay; it's important to recognize that we're DOOMED to uncertainty when we're using inferential statistics. Nonetheless, it's typically better than merely guessing about the population.

Q20)  False       ⇽ As long as the sample is representative, a very large population size is no problem for inferential statistics.

Q21)  True

Q22)  True

Q23)  True

Q24)  True