# Daily Archives: May 20, 2022

## 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….

## If you were to select a person at random, what is the probability that they would have an IQ score of 130 or more, assuming the scores are distributed Normally

If you look at the scores on most IQ tests, they have a mean of 100 and a standard deviation of 15. For class discussion:

(a) Why do you think this is so?

i. This is the natural state of human intelligence.

ii. The tests are engineered to make it so for the convenience of comparison and analysis—questions are modified, added, and subtracted over time, so that the mean score stays at 100 and the standard deviation at 15.

(b) Is “IQ” the same thing as “IQ score?” If not, what is the difference? Homework:

(c) Convert an IQ score of 120 to a z-score.

(d) If you were to select a person at random, what is the probability that they would have an IQ score of 130….

## Dice are small cubes, held in the hand and then dropped or thrown on a flat surface, as part of a game.

Dice are small cubes, held in the hand and then dropped or thrown on a flat surface, as part of a game. Each surface of a die has a number of dots, ranging from one dot to six dots. The number of dots showing on the top surface is said to be how the die lands.

(a) If you throw two dice, is the probability of seeing a “1” on the first die independent of the probability of seeing a “1” on the second die?

(b) If you throw two dice, what is the probability that you will see a “6” on the first die AND a “6” on the second die?

(c) If you throw two dice, what is the probability that you will see a “6”….

## 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….

## A web manager for a retail merchant tests two different presentations of a product to determine whether there is a difference in the length of time that people stay on that product page.

A web manager for a retail merchant tests two different presentations of a product to determine whether there is a difference in the length of time that people stay on that product page. He or she records the visit time in seconds per visitor for 50 visitors for each presentation and finds that people viewing presentation A linger 0.33 seconds longer than those viewing presentation B. From the histogram shown below for a permutation test between the two treatments (putting all 100 values in a hat and repeatedly drawing out pairs of random samples of 50 each), is the observed difference within the range of chance variation?

## 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….

## Answer the following questions referring to the PulseNew.xls data

Answer the following questions referring to the PulseNew.xls data:

(a) Is there any sign that the proportion who ran is different for males versus females? Perform a hypothesis test (resampling or formula), state your conclusion in plain English that would be understandable to someone who never took a statistics course.

(b) Is there evidence here that the “before” pulse rate differs between smokers and nonsmokers? Medical theory suggests that smoking elevates the pulse rate. Perform a hypothesis test (resampling or formula).

(c) We would expect running in place to affect a person’s pulse rate. Test whether before and after pulse rates are the same

## 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,….