Question

climatologist claims that the precipitation in seattle, washington, was greater than in birmingham, alabama, in a recent year. the daily precipitation amounts (in inches) for 30 days in a recent year in seattle and a recent year in birmingham are given in the accompanying table. assume the population standard deviation is 0.247 inch for seattle and 0.523 inch for birmingham. at α = 0.05, can you support the climatologist’s claim? complete parts (a) through (e).
click the icon to view the precipitation data.

(a) identify the claim and state ( h_0 ) and ( h_a ).
what is the claim?
a. the mean precipitation in seattle was greater than in birmingham in a recent year.
b. the mean precipitation in seattle was less than in birmingham in a recent year.
c. the mean precipitation in seattle was the same as in birmingham in a recent year.
d. the mean precipitation in seattle was different than in birmingham in a recent year.
let the data from seattle be sample 1 and let the data from birmingham be sample 2. identify ( h_0 ) and ( h_a ).
( h_0: mu_1 ) dropdown ( mu_2 )
( h_a: mu_1 ) dropdown ( mu_2 )

Explanation:

The claim is that Seattle's mean precipitation (sample 1, \(\mu_1\)) is greater than Birmingham's (sample 2, \(\mu_2\)). The null hypothesis (\(H_0\)) is the opposite or equality, so \(H_0: \mu_1 \leq \mu_2\). The alternative hypothesis (\(H_a\)) supports the claim, so \(H_a: \mu_1 > \mu_2\). For the claim option, A matches the climatologist's statement.

Answer:

The claim: A. The mean precipitation in Seattle was greater than in Birmingham in a recent year.
\(H_0: \mu_1 \leq \mu_2\)
\(H_a: \mu_1 > \mu_2\)