Category Archives: Management

A new synthetic feed additive is found in an experiment to accelerate the growth of hogs sufficiently to reduce the “time to market” by 10%. Should it be added to the feed?

Give your assessment of the relative costs of Type I and Type II errors in the following situations where a decision is pending:

a. A new synthetic feed additive is found in an experiment to accelerate the growth of hogs sufficiently to reduce the “time to market” by 10%. Should it be added to the feed?

b. Researchers examining longitudinal data that have been collected from a large cohort of nurses notice that those who drink more orange juice have a high incidence of asthma. Should consumption of orange juice be discouraged?

c. Analysts for a department store conduct an experiment and find that price tags with multiple successive markdowns that are visible on the tag generate more sales than tags with a single markdown indicated, even though….

A company offers a cloud-sharing service aimed at consumers, including a free level of service to all, as well as higher paying levels.

A company offers a cloud-sharing service aimed at consumers, including a free level of service to all, as well as higher paying levels. Currently, they offer a relatively low level of free service hoping that people will readily see the need for a higher fee-based level. It decides to run an experiment, offering to some extent a higher level of free service hoping that more people will become engaged users and will upgrade. For several weeks, customers are offered either “low” or “high” levels of service, on a random basis, and then the number of upgrades over the next 3 months is tracked. Here are the results:

(a) Calculate the difference between the two conversion rates

(b) Specify a resampling procedure to test whether the difference in….

The “churn” rate in a subscription business is that rate at which subscribers leave in a given time period.

The “churn” rate in a subscription business is that rate at which subscribers leave in a given time period. In the US wireless industry, the churn rate is on the order of 10% annually—out of 100 customers at the beginning of a 12-month period, only 90 will be left at the end of the 12-month period.

(a) A 10% churn rate can be represented by a single box with cards marked 0 and 1. Different sized boxes (i.e., different numbers of cards) can also do the job—give several examples.

(b) What resampling process makes these different boxes functionally equivalent?

– sampling with replacement

– sampling without replacement

(c) Describe the resampling steps that you would take to assess the sampling variability of samples of size 250.

(d) Describe….

This problem concerns the duration of US major league baseball games.

This problem concerns the duration of US major league baseball games. In the early 2000s, Major League Baseball was concerned about the declining television ratings of baseball. One factor considered was the length of games—did they last too long?

For fans of other sports, here is some background relevant to this problem. Baseball has no time limit—the two teams alternate at-bats for a total of nine innings (each team’s at-bat is a half-inning). If the two teams are tied at the end of nine innings, the two teams continue playing until one team is ahead at the end of a full inning. In the National League, pitchers (who are poor hitters) are required to bat. In the American League, the pitcher is not required to hit, and the….

Have you ever wondered, when you weigh yourself on a scale, how the scale is calibrated?

Have you ever wondered, when you weigh yourself on a scale, how the scale is calibrated? How is it known that 150 pounds on that scale is the same as 150 pounds on another? Scales are calibrated by comparison to standard weights. Of course, millions of instruments require calibration and they cannot all be compared to the same weight. Rather, there is a single definitive weight and a hierarchy of other weights that are compared to it. The US National Bureau of Standards maintains a set of standard weights that are an important link in this chain.

In Statistics, Freedman et al. report the results of a set of definitive measurements by the Bureau of one 10 g standard weight, done sometime in 1962–1963. The first measurement was….

A web-based real-estate information and valuation site wants to determine whether it will be worth it to expend time and money to implement a more sophisticated modeling system to estimate home values.

A web-based real-estate information and valuation site wants to determine whether it will be worth it to expend time and money to implement a more sophisticated modeling system to estimate home values. A key question is whether the model is more accurate. A firm conducts an experiment in which it tries out the model and obtains valuations on 15 homes that were recently sold (group A). It also samples 15 other homes from its records that were recently sold (group B). It then compares the valuation error in the two groups. To simplify the analysis, it looks first at the absolute value of the valuation error (not caring about sign).

Valuation error (absolute value in $000)

Group A—35, 15, 17, 4, 13, 22, 19, 43, 33, 21, 5,….

Given the three possible causes of a spike in favorable ratings (restaurant campaign, actual customer sentiment, and random variation) and discuss the role of a hypothesis test in distinguishing among the three causes.

A social media site that allows community members to rate restaurants wants to ensure that the reviews are genuine reviews of the community and not favorable reviews orchestrated by the friends of the restaurant owners. It uses several metrics when examining reviews, one of which is the “percent favorable.” It theorizes that a spike in the percent favorable might represent a campaign by the restaurant, but also recognizes that it might reflect genuine customer sentiment, or just random variation. So it collects 4 days’ worth of such data on a periodic basis and subjects it to a hypothesis test. For one restaurant, the percent favorable has stood at 60% for the last year. One recent 4-day sample showed 72% favorable—23 favorable reviews and 9 unfavorable.

(a) Specify and….

A software service firm has been growing relatively rapidly and concentrating on winning contracts and delivering on them.

A software service firm has been growing relatively rapidly and concentrating on winning contracts and delivering on them. It has paid less attention to getting paid on time, and the investors who own the firm have established a target of $2500, maximum, on the average level of accounts receivable (the average per account, not the total across all accounts). If it is clear that this average is being exceeded, they want a corrective action. On the other hand, they agree with the management that the primary focus should be on winning contracts and delivering on them. So it has been decided to take periodic samples of accounts receivable to watch for clear evidence that the target is being exceeded. Here is the most recent one (in $):

950,….

What would be more reasonable here, to think of height as dependent on age or age dependent on height?

The following questions use this table, which can be downloaded here in Excel format in girls.xls. These data are the heights (in cm) of girls of different ages (in years). For the following questions, you may use software of your choice. (Our source is Siegel and Morgan, Statistics and Data Analysis: An Introduction, 2nd. ed., John Wiley and Sons, 1996. Their source is the 1980 World Almanac)

(a) What would be more reasonable here, to think of height as dependent on age or age dependent on height?

(b) Make a scatterplot of these data and describe what you see.

(c) Find the correlation between these two variables (age and height).

(d) It only makes sense to compute a correlation under certain circumstances. Why is it reasonable here?

….

What is the hypothesized direction of causality? Is this direction confirmed by the results of the hypothesis test?

Activity in the portions of the brain connected with social perception was tracked for a sample of university students, and the number of Facebook friends was recorded for the same sample. (From R. Kanai, B. Bahrami, R. Roylance, G. Rees, “Online social network size is reflected in human brain structure,” Proceedings of the Royal Society B, Published online http://rspb.royalsocietypublishing.org/content/early/2011/10/12/ rspb.2011.1959.full)

Review the data in Brain-Facebook.xls, then

(a) Plot the two variables in a scatterplot.

(b) The metric used for GM density is complex to some extent and it is not necessary to understand it for the purposes of this exercise. However, looking at the scale for GM density, make a guess at how those numbers were calculated. Hint: Review Section 4.4.

(c) Calculate the correlation between brain activity….