Question

Find the P-value.

H0: p=0.1 versus H1: p>0.1 n=250; x=30, α=0.01

Answer #1

Solution :

Given that,

This is the right tailed test .

The null and alternative hypothesis is

H_{0} : p = 0.1

H_{a} : p > 0.1

n = 250

x = 30

= x / n = 30 / 250 = 0.12

P_{0} = 0.1

1 - P_{0} = 1 - 0.1 = 0.9

Test statistic = z

=
- P_{0} / [P_{0
*} (1 - P_{0} ) / n]

= 0.12 - 0.1 / [0.1 - 0.9 / 250 ]

= 1.054

P(z >1.054 ) = 1 - P(z <1.054 ) = 1 - 0.8541 = 0.1459

P-value = 0.1459

= 0.01

P-value ≥

0.1459 ≥ 0.01

Not reject the null hypothesis .

There is insufficient evidence to suggest that.

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