According to Indeed.com, the average annual salary for a sous chef is $46,000. A
ID: 3127511 • Letter: A
Question
According to Indeed.com, the average annual salary for a sous chef is $46,000. A marketing firm claims that a sous chef in Denver makes more than average. In a random sample of 45 sous chefs in Denver, their average salary was $46,500 with a standard deviation of $1,800. At alpha=.05, is this difference significant?
The technical, literary conclusion pair is:
Reject the null, reject the marketing firm's claim that a sous chef in Denver makes more than average
Reject the null, support the marketing firm's claim that a sous chef in Denver makes more than average
Support the null, support the marketing firm's claim that a sous chef in Denver makes more than average
Fail to reject the null, fail to support the marketing firm's claim that a sous chef in Denver makes more than average
A.Reject the null, reject the marketing firm's claim that a sous chef in Denver makes more than average
B.Reject the null, support the marketing firm's claim that a sous chef in Denver makes more than average
C.Support the null, support the marketing firm's claim that a sous chef in Denver makes more than average
D.Fail to reject the null, fail to support the marketing firm's claim that a sous chef in Denver makes more than average
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u <= 46000
Ha: u > 46000
As we can see, this is a right tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = + 1.644853627
Getting the test statistic, as
X = sample mean = 46500
uo = hypothesized mean = 46000
n = sample size = 45
s = standard deviation = 1800
Thus, z = (X - uo) * sqrt(n) / s = 1.863389981
Also, the p value is
p = 0.031203709
As z > 1.6449, and P < 0.05, we REJECT THE NULL HYPOTHESIS.
Hence,
OPTION B: Reject the null, support the marketing firm's claim that a sous chef in Denver makes more than average [ANSWER]