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Chapter 9: Q 103. (page 610)

You are testing H0:μ=10against Ha:μ<10based on an SRS of20

observations from a Normal population. The t statistic is t=−2.25

The P-value

a. falls between 0.01 and 0.02.

b. falls between 0.02 and 0.04.

c. falls between 0.04 and 0.05.

d. falls between 0.05 and 0.25.

e. is greater than 0.25.

Short Answer

Expert verified

The correct option is (a) falls between falls between 0.01 and 0.02

Step by step solution

01

Given information

Sample size(n)=20

Test statistic(t)=−2.25

The null and alternative hypotheses are:

H0:μ=10Ha:μ<10

02

Explanation

According to the alternative hypothesis, the test is one-tailed.

The degree of freedom can be determined using the following formula:

Degreeoffreedom(df)=n−1=20−1=19

The p-value can be calculated as:

P−value=P(t>|t|)=P(t>|−2.25|)=0.018

Thus, it could be said that P-value lies between0.01and0.02

Hence, the correct option is (a).

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