# 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!

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