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Q 104.

Expert-verifiedFound in: Page 610

Book edition
6th

Author(s)
Daren Starnes, Josh Tabor

Pages
837 pages

ISBN
9781319113339

You are testing ${H}_{0}:\mu =10$ against ${H}_{a}:\mu \ne 10$ based on an SRS of $15$

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

$a.t>3.326\phantom{\rule{0ex}{0ex}}b.t>3.286\phantom{\rule{0ex}{0ex}}c.t>2.977\phantom{\rule{0ex}{0ex}}d.t<-3.326ort>3.326\phantom{\rule{0ex}{0ex}}e.t<-3.286ort>3.286$The correct option is (d) $t<-3.326ort>3.326$

Sample size $\left(n\right)=15$

Level of significance $\left(\alpha \right)=0.05$

The null and alternative hypotheses are:

${H}_{0}:\mu =10\phantom{\rule{0ex}{0ex}}{H}_{a}:\mu \ne 10$The degree of freedom is:

$Degreeoffreedom(df)=n-1\phantom{\rule{0ex}{0ex}}=15-1\phantom{\rule{0ex}{0ex}}=14$

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

${t}_{\alpha /2},df={t}_{0.05/2},14\phantom{\rule{0ex}{0ex}}=\pm 3.326$

The test would be significant for the values $t<-3.286$ or $t>3.326$

Hence, the correct option is (d).

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