Question

Two-sided test The one-sample t statistic from a sample of $n=25$observations for the two-sided test of $H_0:\mu =64;H_a:\mu \ne 64$has the value $t=-1.12$.

(a) Find the P-value for this test using (i) Table $B$and (ii) your calculator. What conclusion would you draw at the $5\%$significance level? At the $1\%$significance level?

(b) Redo part (a) using an alternative hypothesis of $H_a:\mu <64$.

Short answer

a. Table B: $0.05<p-value<0.1$. Technology: the P-value is $0.2738.$Fail to reject $H_0$at both levels.

b. Table B: $0.05<p-value<0.1$. Technology: the P-value is $0.1368$. Fail to reject $H_0$at both levels.

Step-by-step solution

Given information

Two-sided test The one-sample t statistic from a sample of $n=25$observations for the two-sided test of $H_0:\mu =64;H_a:\mu \ne 64$has the value$t=-1.12$.

Explanation (part a)

(i) Table $B$: Using Table $B$, we get $0.05<p-value<0.1$

(ii) Calculator: Performing the test with significance level $0.05$,

$p-value:0.27379726$

Decision: There is not enough evidence to reject$H₀$ at the significance level $0.05$, because your p-value is greater than $0.05$.

Performing the test with significance level $0.1$.

$p-value:0.27379726$

Decision: There is not enough evidence to reject$H₀$ at the significance level $0.1$, because your p-value is greater than $0.1$.

Conclusion: Fail to reject $H_0$at both levels.

Explanation (part b)

Redo part (a) using an alternative hypothesis of $H_a:\mu <64$

(i) Table $B$: Using Table $B$, we get $0.05<p-value<0.1$

(ii) Calculator: Performing the test with a significance level$0.05$,

$p-value:0.13689863$

Decision: There is not enough evidence to reject$H₀$ at the significance level $0.05$, because your p-value is greater than $0.05.$

Performing the test with a significance level $0.1$.

$p-value:0.13689863$

Decision: There is not enough evidence to reject$H₀$ at the significance level $0.1,$because your p-value is greater than $0.1$.

Conclusion: Fail to reject $H_0$at both levels.