Question

question 1 (1 point)
a coffee shop owner claims that the average customer wait time is no more than 5 minutes ($muleq5$). a consumer group wants to test if the wait time is actually longer. what are the correct null ($h_0$) and alternative ($h_a$) hypotheses?
$h_0:mu < 5, h_a:mugeq5$
$h_0:muleq5, h_a:mu > 5$
$h_0:mugeq5, h_a:mu < 5$
$h_0:mu = 5, h_a:mu
eq5$
question 2 (1 point)
in a hypothesis test, a p - value of 0.03 is calculated. if the researcher chose a significance level ($alpha$) of 0.05, what is the correct decision?
decrease the significance level to 0.01.
reject the null hypothesis.
accept the alternative hypothesis.
fail to reject the null hypothesis.

Explanation:

Step1: Define null and alternative hypotheses

The null hypothesis ($H_0$) is the claim to be tested. Here, the coffee - shop owner claims $\mu\leq5$, so $H_0:\mu\leq5$. The alternative hypothesis ($H_a$) is what the consumer group wants to test, which is that the wait time is longer, so $H_a:\mu > 5$.

Step2: Recall decision - making rule for hypothesis testing

In hypothesis testing, if the p - value is less than the significance level ($\alpha$), we reject the null hypothesis. Given $p = 0.03$ and $\alpha=0.05$, since $0.03<0.05$, we reject the null hypothesis.

Answer:

Question 1: B. $H_0:\mu\leq5, H_a:\mu > 5$
Question 2: Reject the null hypothesis.