MATH 225N WEEK 7 HYPOTHESIS TESTING
PRACTICE TESTED QUESTIONS 2026 VERIFIED
ANSWER KEY
◉ hypothesis test. Answer: A process that uses sample statistics to
test a claim about the value of a population parameter. (p. 348)
◉ statistical hypothesis. Answer: A statement about a population
parameter. (p. 349)
◉ null hypothesis (*H₀*). Answer: A statistical hypothesis that
contains a statement of equality, such as ≤, =, or ≥. (The symbol *H₀*
is read as "H sub-zero" or "H naught".) (p. 349)
◉ alternative hypothesis (*H*∨*a*). Answer: The complement of the
null hypothesis. It is a statement that must be true if *H₀* is false and
contains a statement of strict inequality, such as >, ≠, or <. (The
symbol *H*∨*a* is read as "H sub-a".) (p. 349)
◉ *(Y.T.I.): Exercise 1 (p. 350):* For the statement below, write the
claim as a mathematical statement. State the null and alternative
hypotheses and identify which represents the claim.
,*A laptop manufacturer claims that the mean life of the battery for a
certain model of laptop is more than 5 hours.*
*Part 1:* Write the claim as a mathematical statement.
A.) μ ≠ 5
B.) μ = 5
C.) μ ≤ 5
D.) μ > 5
E.) μ < 5
F.) μ ≥ 5
*Part 2:* Choose the correct null and alternative hypotheses below.
A.) *H₀*: μ = 5
*H*∨*a*: μ ≠ 5
B.) *H₀*: μ ≠ 5
*H*∨*a*: μ = 5
C.) *H₀*: μ > 5
*H*∨*a*: μ ≤ 5
D.) *H₀*: μ ≥ 5
*H*∨*a*: μ < 5
E.) *H₀*: μ < 5
*H*∨*a*: μ ≥ 5
,F.) *H₀*: μ ≤ 5
*H*∨*a*: μ > 5
*Part 3:* Identify which is the claim.
A.) The alternative hypothesis *H*∨*a*: μ ≠ 5 is the claim.
B.) The null hypothesis *H₀*: μ ≤ 5 is the claim.
C.) The alternative hypothesis *H*∨*a*: μ > 5 is the claim.
D.) The null hypothesis *H₀*: μ ≥ 5 is the c. Answer: Correct
Answers:
*Part 1:* D.) μ > 5
*Part 2:* F.) *H₀*: μ ≤ 5
*H*∨*a*: μ > 5
*Part 3:* C.) The alternative hypothesis *H*∨*a*: μ > 5 is the claim.
(Section 1)
◉ Type I error. Answer: Occurs if the null hypothesis is rejected
when it is true. (p. 351)
◉ Type II error. Answer: Occurs if the null hypothesis is not rejected
when it is false. (p. 351)
, ◉ *(Y.T.I.): Exercise 2 (p. 351):* Describe type I and type II errors for
a hypothesis test of the indicated claim.
*A furniture store claims that no more than 80% of its new
customers will return to buy their next piece of furniture.*
*Part 1:* Describe the type I error. Choose the correct answer below.
A.) A type I error will occur when the actual proportion of new
customers who return to buy their next piece of furniture is no more
than 0.80, but you reject *H₀*: p ≤ 0.80.
B.) A type I error will occur when the actual proportion of new
customers who return to buy their next piece of furniture is no more
than 0.80, but you fail to reject *H₀*: p ≤ 0.80.
C.) A type I error will occur when the actual proportion of new
customers who return to buy their next piece of furniture is at least
0.80, but you reject *H₀*: p ≥ 0.80.
D.) A type I error will occur when the actual proportion of new
customers who return to buy th. Answer: Correct Answers:
*Part 1:* A.) A type I error will occur when the actual proportion of
new customers who return to buy their next piece of furniture is no
more than 0.80, but you reject *H₀*: p ≤ 0.80.
*Part 2:* A.) A type II error will occur when the actual proportion of
new customers who return to buy their next piece of furniture is
more than 0.80, but you fail to reject *H₀*: p ≤ 0.80.
PRACTICE TESTED QUESTIONS 2026 VERIFIED
ANSWER KEY
◉ hypothesis test. Answer: A process that uses sample statistics to
test a claim about the value of a population parameter. (p. 348)
◉ statistical hypothesis. Answer: A statement about a population
parameter. (p. 349)
◉ null hypothesis (*H₀*). Answer: A statistical hypothesis that
contains a statement of equality, such as ≤, =, or ≥. (The symbol *H₀*
is read as "H sub-zero" or "H naught".) (p. 349)
◉ alternative hypothesis (*H*∨*a*). Answer: The complement of the
null hypothesis. It is a statement that must be true if *H₀* is false and
contains a statement of strict inequality, such as >, ≠, or <. (The
symbol *H*∨*a* is read as "H sub-a".) (p. 349)
◉ *(Y.T.I.): Exercise 1 (p. 350):* For the statement below, write the
claim as a mathematical statement. State the null and alternative
hypotheses and identify which represents the claim.
,*A laptop manufacturer claims that the mean life of the battery for a
certain model of laptop is more than 5 hours.*
*Part 1:* Write the claim as a mathematical statement.
A.) μ ≠ 5
B.) μ = 5
C.) μ ≤ 5
D.) μ > 5
E.) μ < 5
F.) μ ≥ 5
*Part 2:* Choose the correct null and alternative hypotheses below.
A.) *H₀*: μ = 5
*H*∨*a*: μ ≠ 5
B.) *H₀*: μ ≠ 5
*H*∨*a*: μ = 5
C.) *H₀*: μ > 5
*H*∨*a*: μ ≤ 5
D.) *H₀*: μ ≥ 5
*H*∨*a*: μ < 5
E.) *H₀*: μ < 5
*H*∨*a*: μ ≥ 5
,F.) *H₀*: μ ≤ 5
*H*∨*a*: μ > 5
*Part 3:* Identify which is the claim.
A.) The alternative hypothesis *H*∨*a*: μ ≠ 5 is the claim.
B.) The null hypothesis *H₀*: μ ≤ 5 is the claim.
C.) The alternative hypothesis *H*∨*a*: μ > 5 is the claim.
D.) The null hypothesis *H₀*: μ ≥ 5 is the c. Answer: Correct
Answers:
*Part 1:* D.) μ > 5
*Part 2:* F.) *H₀*: μ ≤ 5
*H*∨*a*: μ > 5
*Part 3:* C.) The alternative hypothesis *H*∨*a*: μ > 5 is the claim.
(Section 1)
◉ Type I error. Answer: Occurs if the null hypothesis is rejected
when it is true. (p. 351)
◉ Type II error. Answer: Occurs if the null hypothesis is not rejected
when it is false. (p. 351)
, ◉ *(Y.T.I.): Exercise 2 (p. 351):* Describe type I and type II errors for
a hypothesis test of the indicated claim.
*A furniture store claims that no more than 80% of its new
customers will return to buy their next piece of furniture.*
*Part 1:* Describe the type I error. Choose the correct answer below.
A.) A type I error will occur when the actual proportion of new
customers who return to buy their next piece of furniture is no more
than 0.80, but you reject *H₀*: p ≤ 0.80.
B.) A type I error will occur when the actual proportion of new
customers who return to buy their next piece of furniture is no more
than 0.80, but you fail to reject *H₀*: p ≤ 0.80.
C.) A type I error will occur when the actual proportion of new
customers who return to buy their next piece of furniture is at least
0.80, but you reject *H₀*: p ≥ 0.80.
D.) A type I error will occur when the actual proportion of new
customers who return to buy th. Answer: Correct Answers:
*Part 1:* A.) A type I error will occur when the actual proportion of
new customers who return to buy their next piece of furniture is no
more than 0.80, but you reject *H₀*: p ≤ 0.80.
*Part 2:* A.) A type II error will occur when the actual proportion of
new customers who return to buy their next piece of furniture is
more than 0.80, but you fail to reject *H₀*: p ≤ 0.80.
