A credit card company claims that the mean credit card debt for individuals is greater than $5,000. You want to test this claim. You find that a random sample of 26 cardholders has a mean credit card balance of $5,274

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 22SGR
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Question
A credit card company claims that the mean credit card debt for individuals is greater than
$5,000.
You want to test this claim. You find that a random sample of
26
cardholders has a mean credit card balance of
$5,274
and a standard deviation of
$600.
At
α=0.01​,
can you support the​ claim? Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.
 
 
 

Question content area bottom

Part 1
​(a) Write the claim mathematically and identify
H0
and
Ha.
 
Which of the following correctly states
H0
and
Ha​?
 
 
A.
H0​:
μ≤​$5,000
Ha​:
μ>​$5,000
Your answer is correct.
 
B.
H0​:
μ>​$5,000
Ha​:
μ≤​$5,000
 
C.
H0​:
μ=​$5,000
Ha​:
μ>​$5,000
 
D.
H0​:
μ=​$5,000
Ha​:
μ≠​$5,000
 
E.
H0​:
μ≥​$5,000
Ha​:
μ<​$5,000
 
F.
H0​:
μ>​$5,000
Ha​:
μ≤​$5,000
Part 2
​(b) Find the critical​ value(s) and identify the rejection​ region(s).
 
What​ is(are) the critical​ value(s),
t0​?
 
t0=enter your response here
 
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