Page 67 - Basic Statistics

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b. If both the population variance is unknown but n1  30 and n2  30, then

X X −
Z = 1 2 ( N4 )
σ ˆ
X 1 − X 2

Testing criteria:

If this test use significance level  , then

H0 is accepted if Z-actual  - Z-table or Pr ( Z  z actual )   , otherwise

H0 is rejected if Z-actual < - Z-tabel or Pr ( Z  z actual ) <  .

Worked Example 4.4:

A golf ball factory introduced the latest production of golf balls (new
type), and declared better than the old golf balls (old type). Distance of the two

types of golf balls each having standard deviation : old type 1 = 9.8 meters and

a new type 2 = 7.1 meters. A golfer wants to test the above statement by

selected at random, hits 35 shots using balls of old types and hits 35 shots using

balls of new types. Mean of distance in metres for each type respectively 20.1
meters and 23.6 meters. By using Significance level  = 0.05, test the hypotheses

that:

a. Both types of golf balls are not different

b. The old type is inferior to the new type.

Worked Solution:

1 = 9.8 meter 2 = 7.1 meter
X = 20.1 meter X = 23.6 meter
2
1
n1 = 35 n2 = 40

~~* CHAPTER 4 TESTING HYPOTHESIS *~~