One-sided test Suppose you carry out a significance test of $H_0:\mu =5$versus $H_a:\mu >5$based on a sample of size $n=20$and obtain $t=1.81$.

(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$H_a:\mu \ne 5$.

(One-sided test Suppose you carry out a significance test of $H_0:\mu =5$versus $H_a:\mu >5$based on a sample of size $n=20$and obtain $t=1.8$.

(i) Table $B$:

The degrees of freedom required for looking Table $B$: is given by $df=n-1=20-1=19$

Now for a one tailed significance t test looking at Table $B$: the p-value is calculated as

localid="1651324003883" $0.025<P-value<0.05$

(ii) Calculator:

Performing test on significance level $0.05$: $p-value:0.04388018$

Decision: You can reject$H₀$at the significance level $0.05$, because your p-value does not exceed $0.05$.

Performing test on significance level $0.1:$$p-value:0.9561198$

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: Reject $H_0$ at the $5\%$significance level. Fail to reject $H_0$at the $1\%$significance level.

Redo part (a) using an alternative hypothesis of $H_a:\mu \ne 5$

(i) Table $B$:

The degrees of freedom required for looking Table $B$: is given by

$df=n-1=20-1=19$

Now for a one tailed significance t test looking at Table $B$: the p-value is calculated as

$0.05<P-value<0.1$

(ii) Calculator:

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 test on significance level $0.1$: $p-value:0.08776036$

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