Page 68 - Basic Statistics

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(a) The test requires a two-tailed test:

Hypotheses: H0 : μ = μ
2
1
H1 : μ  μ
1
2

Significance level:  = 0.05
σ 2 σ 2
Standard deviation: σ = 1 + 2
X 1 − X 2 n n
1 2
(9.8) 2 (7.1) 2
= + = 2.0
35 40

X X −
Z = 1 2
σ
X 1 − X 2

20.1− 23.6
= = -1.75
2.0

In the standard normal table;  Z/2 =  1.96

Conclusion:  Z  < Z/2, ie 1.75 < 1.96, so not enough evidence to reject H0. We

conclude that there is no significant different of both types of golf balls.

b) This the test requires one-tailed test:

Hypotheses: H0 : μ = μ
1
2
H1 : μ < μ
2
1

Significance level:  = 0.05

In the standard normal table; - Z = - 1.64
Conclusion: Z < - Z-table, ie - 1.75 < -1.64, so H0 is rejected at the 5 percent

significance level. We conclude that the old type is inferior to the new type.

~~* CHAPTER 4 TESTING HYPOTHESIS *~~