Question

An information technology manager claims that her servers have a daily error rate that does not exceed 5%. In order to test this claim, a sample of 100 days of operation finds that the servers suffered from an error on 8 days. The researcher determines a level of significance equal to 0.05.

Is this a right, left, or two-tailed hypothesis test? A) Left-tailed B) Right-tailed C) Two-tailed

What is ?̂equal to? A) 0.01 B) 0.05 C) 0.08 D) 20 E) 100

What is the z-score of the sample? A) 1.38 B) -0.87 C) 3.46 D) 2.23

What is the p-value of the sample? A) 0.084 B) 0.807 C) 0.001 D) 0.013

What would you conclude about this hypothesis test? A) Fail to reject null hypothesis. B) Accept the null hypothesis. C) Reject the null hypothesis. D) Accept the alternate hypothesis.

Answer #1

Solution :

The null and alternative hypothesis is

H_{0} : p = 0.05

H_{a} : p < 0.05

x = 8

n = 100

This is left tailed test

= x / n = 8 / 100 = 0.08

P_{0} = 0.05

1 - P_{0} = 1 - 0.05 = 0.95

Test statistic = z

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

= 0.08 - 0.05/ [(0.05 * 0.95) / 100]

z = 1.38

P(z > 1.38) = 1 - P(z < 1.38) = 1 - 0.916

P-value = 0.084

= 0.05

P-value >

Fail to reject null hypothesis .

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