A courier company claims that the median delivery time for local packages is $30$ minutes. In a random sample of $15$ deliveries, the recorded times (in minutes) were:
$28,31,30,29,32,35,30,33,29,36,34,30,37,38,30$
i) Identify the claim and state $H_0$ and $H_a$.
ii) At the $0.05$ significance level, can you reject the company’s claim? Interpret the decision.

i) $H_0:\tau =30$; $H_a:\tau >30$

ii) Fail to reject $H_0$. At the $5\%$ significance level, there is insufficient evidence to conclude that the true median delivery time exceeds $30$ minutes.

i) $H_0:\tau =30$; $H_a:\tau \ne 30$

ii) Reject $H_0$. At the $5\%$ significance level, there is sufficient evidence to conclude that the true median delivery time differs from $30$ minutes.

i) $H_0:\tau =30$; $H_a:\tau \ne 30$

ii) Fail to reject $H_0$. At the $5\%$ significance level, there is insufficient evidence to conclude that the true median delivery time differs from $30$ minutes.

i) $H_0:\tau =30$;

ii) Fail to reject $H_0$. At the $5\%$ significance level, there is insufficient evidence to conclude that the true median delivery time is less than $30$ minutes.