# Rochester Institute of Technology Variables & Statistics Worksheet

An electrical engineer must design a circuit to deliver the maximum amountof current to a display tube to achieve sufficient image brightness. Within

her allowable design constraints, she has developed two candidate circuits

and test prototypes of each. The resulting data (in microamperes) are as

follows:

Circuit 1:

Statistics

Circuit 2:

255

255

258

257

253

251

2541

254

250

Sum of

Variable Sum Squares

Circuit 1: 2287.00 581205.00

Circuit 2: 2025.00 512659.00

250

252

249

256

257

252

258

251

Test for evidence that first circuit can deliver a higher current that circuit 2

using a 10% level.

Show all work for this problem!Question 2 (1 point)

The percentage of titanium in an alloy used in aerospace castings is measured in 41

randomly selected parts. The sample deviation in these parts is 0.29. Use this information

to test for the hypothesis that the true deviation in the percentage of titanium different from

0.25 using a 5% level of significance. Show all work for this problem!Question 3 (1 point)

Cloud seeding has been studied for many decades as a weather modification procedure. The

rainfall in acre-feet from 20 clouds that were selected at random and seeded with silver

nitrate follows:

18.0 30.7

31.9

27.1

Statistics

19.8 27.1 22.3

25.0

24.7 26.9

Sum of

Variable Sum Squares

Rainfall 520.70 13991.41

18.8 31.8 23.4 21.2 27.9

21.8 29.2 34.8 26.7 31.6

Can you support the claim that the mean rainfall from seeded clouds is not 25 acre-feet?

Use a 1% level of significance, you may assume the distribution of rainfall follows a normal

distribution. Show all work for this problem!Supercavitation is a propulsion technology for undersea vehicles that can greatly increase

their speed. It occurs above approximately 50 meters per second when pressure drops

sufficiently to allow the water to dissociate into water vapor, forming a gas bubble behind

the vehicle. When the gas bubble completely encloses the vehicle, supercavitation is said to

occur. 10 tests were conducted on a scale model of an undersea vehicle in a towing basin

with the average observed speed of 102.7 meters per second. Assume that speed is

normally distributed with a known true standard deviation of 4.3 meters per second. Test

the hypotheses that the true mean is equal to 100 meters per second vs the alternative that

the mean is higher. Show all work for this problem!