# Math Phase II

Equations did not copy/paste right so do not refer to this page to do the assignment, as you know of course. 🙂 Refer to attached document/pdf.

For the project you should identify three research questions that can be addressed through different hypothesis testing procedures. Your submission should include the following components.

1. Introduction: Briefly describe (in words) each of the three research questions and your motivation for studying them (not more than two pages). For each test you should state your null hypothesis and alternative hypothesis.

2. Hypothesis tests: for each of the three tests clearly discuss: (1) the data used to conduct the test, (2) any assumption that you need to make in order to conduct the test including support for making these assumptions, (3) the test and its results, (4) the statistical significance of your findings.

3. Summary: summarize your findings form the analysis. What do you conclude about the hypothesis you raised? Identify key limitations of your analysis (including any limitations of the data set), contributions that you believe your analysis makes to the readers, and any interesting directions for future analysis (not more than three pages)

Project sample is shown as below:

Introduction: The Doll Computer Company makes its own computers and delivers them directly to customers who order them via the Internet.

To achieve its objective of speed, Doll makes each of its five most popular computers and transports them to warehouses from which it generally takes 1 day to deliver a computer to the customer.

This strategy requires high levels of inventory that add considerably to the cost.

To lower these costs the operations manager wants to use an inventory model. He notes demand during lead time is normally distributed and he needs to know the mean to compute the optimum inventory level.

He observes 25 lead time periods and records the demand during each period.

The manager would like a 95% confidence interval estimate of the mean demand during lead time. Assume that the manager knows that the standard deviation is 75 computers

Hypothesis Tests:

25 observed lead time shown below

235 374 309 499 253

421 361 514 462 369

394 439 348 344 330

261 374 302 466 535

386 316 296 332 334

Interpret the question

· X represents demand

a. X~N (µ,75)

· δ x =75 (standard deviation)

· n=25

· We would like to create a 95% confidence interval for the mean demand based on our sample of 25 lead time periods

· What do we need to know?

x̄ + Z α/2

· Compute the sample mean (X-bar) = 370.16

· Finding Z α/2

a. Looking for Z α/2 such that:

b. P (- Zα/2<Z< Zα/2) =0.95

c. Easiest:

Look for the lower tail probability in the normal table

P(Z<-Z α/2 )=0.025

d. Therefore:

Z α/2= 1.96

The computation is not done, but the format is pretty much like shown above.