(1.) You are considering buying a copy machine for your office. You don't want to buy such a machine if the demand isn't large enough to justify the extra cost of a high volume machine. The salesman lets you test the machine for 30 working days and over this time you find that the average number of pages photocopied per day was 2650 with a standard deviation of 453 pages. You also determine that the distribution of copier demand appears to be normal.

Your finance people tell you that based upon the price differential between the cheaper "medium volume" photocopier and the "high volume" photocopier, it only makes economic sense to buy the high volume machine if mean demand exceeds 2450 photocopied pages per day.

(a) Based upon this information alone, perform a one-sided hypothesis at a 1% level of significance. Should you purchase the high volume machine?

(b) Create the appropriate 99% confidence interval for this problem. Do you arrive at the same conclusion as in Part (a) above?

(2.) Your company is considering adopting new manufacturing procedures. You decide to compare the productivity of employees in your factory in Rochester, New York (Plant #1) with the employees in Oak Ridge, Tennessee (Plant #2). You take the following sample data drawn at random from each of the factories:

	# Employees	Average Productivity (units / hour)	Sample Standard Deviation
Plant #1	45	8.61	3.69
Plant #2	55	6.15	6.17

Based upon sample data, it looks like Plant #1 may have the best operating procedures. But is it really true, i.e. are the population means different?

(a) Perform a two-sided hypothesis test for estimating if there is a difference between the average productivity of the two factories. At a 5% level of significance, can you conclude that employee productivity is different?

(b) Create the appropriate 95% confidence interval for this problem. Do you arrive at the same conclusion as in Part (a) above?

(3.) A health researcher wants to investigate the claims being made by a manufacturer of miracle weight reduction pills. To determine whether the pills actually reduce weight, the researcher has the time and budget to randomly select eleven people and record their weight before they begin taking the pills and their weight after they take the pills for the minimum number of days recommended by the manufacturer. The results are given in the table below:

Person #	Weight Before Taking Pills (lbs)	Weight After Taking Pills (lbs)
1	198	193
2	256	262
3	212	204
4	245	241
5	185	179
6	196	204
7	217	209
8	188	185
9	237	237
10	253	244
11	199	192

(a) Based upon this information alone, perform the appropriate hypothesis test and determine, at a 2.5% level of significance, whether the use of the pills is linked to a statistically significant reduction in weight.

(b) Create the appropriate 97.5% confidence interval for this problem. Do you arrive at the same conclusion as in Part (a) above?

(4.) Your marketing and financial analyses indicate that, all other things being equal, if a new product achieves a market share of 40% or more, it will be successful.

You create a focus group of 300 randomly selected potential customers and discover that 135 of them said that they would buy the product.

(a) Based upon this information alone, perform the appropriate hypothesis test and determine, at a 5% level of significance, whether your company should introduce this new product.

(b) Create the appropriate 95% confidence interval for this problem. Do you arrive at the same conclusion as in Part (a) above?

(5.) Perform the appropriate hypothesis test for determining whether there is a difference in the proportion of large retailers that use advanced statistical forecasting techniques and small retailers that use advanced statistical forecasting techniques. You have the following sample data:

	Sample Size	# That Used Adv. Statistical Forecasting Techniques
Large Retailers	112	70
Small Retailers	135	65

(a) Perform the appropriate hypothesis test to determine if there is a difference. Assume a 10% level of significance.

(b) Create the appropriate 90% confidence interval for this problem. Do you arrive at the same conclusion as in Part (a) above?

(6.) You are considering the purchase of an expensive passive solar heating device which the seller claims will be effective in reducing your monthly home heating expenses.

Before you buy this device, you survey 40 randomly selected homes in your area that have already purchased the device. You ask each homeowner what their monthly heating expenses were before they purchased the device and their monthly heating expenses after the solar heating device was installed.

The results are in the following table:

Home #	Mo. Heating Bill Without Passive Solar System ($)	Mo. Heating Bill With Passive Solar System ($)
1	252	248
2	256	262
3	218	236
4	297	309
5	265	236
6	260	259
7	298	299
8	254	252
9	293	285
10	221	199
11	279	266
12	261	264
13	228	218
14	200	219
15	269	249
16	299	283
17	280	251
18	263	273
19	251	251
20	206	223
21	292	301
22	254	244
23	212	187
24	250	256
25	247	238
26	276	293
27	246	222
28	282	267
29	202	194
30	260	243
31	243	261
32	288	284
33	262	266
34	267	261
35	250	240
36	251	256
37	218	220
38	250	243
39	286	257
40	277	267

(a) Perform the appropriate hypothesis test to determine if the use of the passive solar heating device can be attributed to lower monthly heating expenses

Assume a significance level of 2%.

(b) Assume that the solar heating equipment costs $3,000 to buy and install. Using the appropriate 98% confidence interval, calculate how many years it will take you to "break even" if you make this investment (ignore the Time Value Of Money)