A sample of $12$ college students has an average monthly rent of $\mathrm{\backslash (}850$ with a sample standard deviation of $\mathrm{\backslash )}120$. Test the claim that the average rent is greater than $\$800$ at the $0.05$ significance level. What are the test statistic and the critical value for this right-tailed test?

Test Statistic: $t=1.443$

Critical Value: $t_{crit}=1.796$

Conclusion: Fail to reject the null hypothesis; there is not enough evidence to support the claim.

Test Statistic: $t=2.015$

Critical Value: $t_{crit}=1.796$

Conclusion: Reject the null hypothesis; there is enough evidence to support the claim.

Test Statistic: $t=1.443$

Critical Value: $t_{crit}=1.796$

Conclusion: Reject the null hypothesis; there is enough evidence to support the claim.

Test Statistic: $t=1.443$

Critical Value: $t_{crit}=1.282$

Conclusion: Fail to reject the null hypothesis; there is not enough evidence to support the claim.