## Characterizing Uncertainty

Characterizing Uncertainty

Consider the following:

Many business activities generate data that can be thought of as random. An example described in the textbook is the servicing of cars at an oil change shop. Each car entering the shop can be considered an experiment with random outcomes. A variable of interest in this experiment could be the amount of time necessary to service the car. Service time will vary randomly with each car.

Often times we can capture the most relevant characteristics of a stochastic process with a simple probability distribution model. We can then analyze the model to make predictions and drive decisions. For instance, we could estimate the number of technicians the oil change shop needs to service demand on a Saturday afternoon.

Respond to the following questions:
o What is a random variable?
o How would you differentiate a discrete from a continuous random variable?

A laptop manufacturing company has implemented a 2-step process to test the quality of each production batch. In the first step, a technician randomly selects 15 laptops from the batch and determines whether they meet specifications. The batch is considered acceptable provided no more than 1 laptop fails to meet specifications. Otherwise, the entire batch has to be tested in the second step. Historical data shows that 95% of the laptops produced adhere to specifications.
o What are the 4 characteristics of a binomial experiment?
o Can we use a binomial distribution to model this process?
o What is the probability that the entire batch unnecessarily has to be tested if in fact 95% of its laptops conform to specifications? (Hint: Use Excel’s =BINOMDIST() function to find the probability)
o What is the probability that the batch is incorrectly accepted if only 75% of its laptops actually conform to specifications?

Write a response in a minimum of 500 words.

Testing Hypotheses

Hypothesis testing is used in business to test assumptions and theories. These assumptions are tested against evidence provided by actual, observed data. A statistical hypothesis is a statement about the value of a population parameter that we are interested in. Hypothesis testing is a process followed to arrive at a decision between 2 competing, mutually exclusive, collective exhaustive statements about the parameter’s value.

Consider the following scenario. An industrial seller of grass seeds packages its product in 50-pound bags. A customer has recently filed a complaint alleging the bags are under filled. A production manager randomly samples a batch and measures the following weights:

Weight (lbs)
45.6 49.5
47.7 46.7
47.6 48.8
50.5 48.6
50.2 51.5
46.9 50.2
47.8 49.9
49.3 49.8
53.1 49.3
49.5 50.1

To determine whether the bags are indeed being underfilled by the machinery, the manager has to conduct a test of mean with a significance level α = 0.05.

Write a response to the following in a minimum of 500 words:
• State appropriate null (Ho) and alternative (H1) hypotheses.
• What is the critical value if we work with a significant level α = 0.05.
• What is the decision rule?
• Calculate the test statistic.
• Are the bags indeed being under-filled?
• Should be machinery be recalibrated? 