The average room rate for a hotel in a city in 2016 was $348. Suppose the city's Chamber of Commerce would like to
test if this rate has changed recently by randomly sampling 52 room rates. The mean of this sample was found to be
$361.34. Assume the population standard deviation is $56. Using $\alpha = 0.05$, complete parts a through c.
a. State the null and alternative hypothesis.
Let $\mu$ be the population mean. Determine the null hypothesis, $H_0$, and the alternative hypothesis, $H_1$.
$H_0: \mu = 348$
$H_1: \mu \neq 348$
(Type integers or decimals. Do not round. Do not include the $ symbol in your answers.)
b. What conclusions can be drawn for this test?
Identify the critical value.
$z_{\alpha/2} = 1.96$
(Round to two decimal places as needed.)
Calculate the appropriate test statistic.
$z_x = \boxed{}$ (Round to two decimal places as needed.)