# Statistics

The problem is to estimate that sales for the coming year for a maker of industrial equipment. The forecast is based on askingcustomers how much they are planning to order next year. To use the research budget efficiently, the customers are stratisifiedby the size of their orders during the past year. The following is some relevant information based on the past year"

Strata Customer Size Proportion Standard Deviation Interview Cost

Large 0.1 40 64

Medium 0.2 3 64

Small 0.7 2 64

Number of customers 5,000

A. Assume that a total of 300 interviews are to be conducted. How would you allocate those interviews among the three strata?

B. If a simple random sample of size 300 were obtained from the population, about 10 percent, or 30 interviews, would be from large customers stratum. Why did you recommend in part (a) that more than 30 interview be conducted from this stratum?

C. The survey was conducted, and the average values (in thousands) for each stratum were as follows:

X1=100

X2=8

X3=5

What would your estimate be of the population mean, the average sales that will be received from all customers next year?

D. Given the context of part ( c ) what would be the variance of your estimate of the population mean? Do you think that this variance would be larger or smaller than the variance of your estimate of the population mean if you had taken a simple random sample of size 300 from the total population? Why?

E. What is the total interviewing cost, given a cost per interview of $64, and 300 interviews?

F. Assume now that it has been decided that the small customers can be contacted by phone, making their cost per interview only $9 each. Repeat the analysis that you did in part ( a). How would you allocate 300 interviews now?

G. Now under part (f) what is the total interviewing cost?

H. How many interviews could you conduct, assuming that you had the same amount of money determined under part (e), that you allocated the interviews according to your answer in part (f) and that the costs were as in part (f)?

© BrainMass Inc. brainmass.com October 25, 2018, 3:48 am ad1c9bdddfhttps://brainmass.com/statistics/dispersion-and-spread-of-data/statistics-354268

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.

Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]

having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).

Demonstrate that the mle theta;hat is a sufficient statistic for theta;.

Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

View Full Posting Details