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Chapter 9: Q 104. (page 610)

You are testing H0:μ=10 against Ha:μ≠10 based on an SRS of 15

observations from a Normal population. What values of the t statistic are statistically significant at the α=0.005 level?

a.t>3.326b.t>3.286c.t>2.977d.t<−3.326ort>3.326e.t<−3.286ort>3.286

Short Answer

Expert verified

The correct option is (d) t<−3.326ort>3.326

Step by step solution

01

Given information

Sample size (n)=15

Level of significance (α)=0.05

The null and alternative hypotheses are:

H0:μ=10Ha:μ≠10
02

Explanation

The degree of freedom is:

Degreeoffreedom(df)=n−1=15−1=14

The critical value at a 5% significance level and 14 degrees of freedom can be calculated using the critical value table as follows:

tα/2,df=t0.05/2,14=±3.326

The test would be significant for the values t<−3.286ort>3.326

Hence, the correct option is (d).

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Most popular questions from this chapter

Watching grass grow The germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of grass seed usually has a germination rate of 0.80. A company wants to see if spraying the seeds with a chemical that is known to increase germination rates in other species will increase the germination rate of this variety of grass. The company researchers spray a random sample of 400grass seeds with the chemical, and 339of the seeds germinate. Do these data provide convincing evidence at the α=0.05 significance level that the chemical is

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d. You can carry out the test only if the population standard deviation is known.

e. You can safely carry out the test if your sample size is at least 30 .

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