Number 3 (499)

2. The Kolmogorov-Smirnov one-sample test can be used to test a set of data for normality. In reviewing math test data from 35 second grade students, the critical value of 0.05 was compared to the obtained p-value of 0.023. Interpret the results by determining if the null hypothesis can be rejected, and state whether a parametric or nonparametric procedure should be used with this sample. Provide a brief, but complete response.

3. Statisticians often turn to nonparametric measures when a set of data do not meet specific requirements. From the list below, select all requirements that must be met in order to use parametric statistics.

a. approximately resemble a normal distribution

b. consist of independent observations, except for paired values

c. small sample

d. have approximately equal variances

e. consist of values on a nominal or ordinal measurement scale

4. The approach of mathematics has changed over the years. Describe how the approach of mathematics began starting in Ancient Babylonia, and then discuss how it changed during the time of the Ancient Greeks. Then, compare this to how mathematics is approached today. Be specific in your description and explanation.

5. Essay: In conducting a multiple linear regression analysis, an R2 value of 0.46 is obtained. An extra variable is added and R2 improves to 0.52. The analyst conducting the regression analysis concludes that this is a meaningful increase in R2 and determines that the latter model is an appropriate model to be used. What cautions would you suggest to this analyst with respect to using R2 in this situation?  

6. Hyce Pesticides has launched a new ad campaign. Being that they are the only pesticide company in the region, the company’s research department believes that 40% of the customers who currently do not use Hyce will buy it the next time they need a pesticide. Other researchers studied customer loyalty associated with Hyce. These studies found that 80% of the customers who use Hyce will by it again the next time they need a pesticide. Show all your work when answering the following questions. Complete all 7 parts (a thru g).

(a) Write the data provided in probability form and write the complements.

P(next purchase is Hyce|current purchase is Hyce) = ___

P(next purchase is not Hyce|current purchase is Hyce) = ___

P(next purchase is Hyce|current purchase is not Hyce) = ___

P(next purchase is not Hyce|current purchase is not Hyce) =___

(b) Why is this process considered a Markov Proccess?

(c) The following is the Transition diagram for Hyce Industries. Properly label the diagram below.

Buy Hyce

State 1

Not Buy Hyce

State 2

(d) Develop the transition matrix for the diagram above.

(e) In a longitudinal study, it is found that Hyce there is a 25% chance that a person is in the market for their particular type of cleaning solution (Market Share). This information provided Hyce Industries with the initial conditions it needed. The initial conditions probability matrix is P = [___, ____]

(f) Use the Matrices in parts d and e to find the market share after the third following purchase.

(g) What is the steady state for Hyce Industries market share?

7. Use the data in the worksheet Customer Data in the Excel workbook That file is named MATH499_MATH325_Data.xlsx That file includes the monthly sales totals from a random sample of 38 stores in a nation-wide chain of sporting goods stores. All stores in the chain are approximately the same size and carry essentially the same merchandise. Additional information is also provided in this dataset regarding the customer base for each of the 38 stores in the sample. Answer all 4 parts of this question.

a. Assuming there is a linear relationship between monthly sales and the median family income, formulate a simple linear regression model that estimates the relationship between monthly sales (Y) and median family income (X). Place your regression equation in the space below.