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Question 1
A quality inspector wants to test whether the mean lifetime of a batch of light bulbs differs from the manufacturer's claim of 1200 hours. She samples 20 bulbs but does not know the population standard deviation. Which test should she use?
No clue? Show me the answer
Correct answerCorrect!Incorrect
AOne-sample t-test
Step-by-step walkthrough
Choose a solution method
Method #1Worked solution
Step 1: Identify what is known
The population standard deviation $σ$ is not known; only sample data is available.
Step 2: Apply the decision rule
The rule is: unknown $σ$ $\to$ t-test, regardless of sample size.
Step 3: Check sample structure
There is only one sample of 20 bulbs being compared to a single hypothesised value of 1200 hours, so it is a one-sample test.
Step 4: Conclude
Since $σ$ is unknown and there is one sample compared to a fixed value, a one-sample t-test is appropriate.
Method #2Why the others are wrong
Step 1: Option A
A z-test requires $σ$ to be known; here it is not, so this is incorrect.
Step 2: Option C
A two-sample t-test compares two independent groups, but there is only one sample here.
Step 3: Option D
A paired t-test requires two related measurements per subject; there is no pairing described.
Step 4: Select correct answer
The one-sample t-test is correct since $σ$ is unknown.
Question 2
Which statement about Type I and Type II errors is correct?
No clue? Show me the answer
Correct answerCorrect!Incorrect
BA Type I error is rejecting a true $H_{0}$

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14 more questions in this topic

Free preview 2/16

Question 1
A quality inspector wants to test whether the mean lifetime of a batch of light bulbs differs from the manufacturer's claim of 1200 hours. She samples 20 bulbs but does not know the population standard deviation. Which test should she use?
No clue? Show me the answer
Correct answerCorrect!Incorrect
AOne-sample t-test
Step-by-step walkthrough
Choose a solution method
Method #1Worked solution
Step 1: Identify what is known
The population standard deviation $σ$ is not known; only sample data is available.
Step 2: Apply the decision rule
The rule is: unknown $σ$ $\to$ t-test, regardless of sample size.
Step 3: Check sample structure
There is only one sample of 20 bulbs being compared to a single hypothesised value of 1200 hours, so it is a one-sample test.
Step 4: Conclude
Since $σ$ is unknown and there is one sample compared to a fixed value, a one-sample t-test is appropriate.
Method #2Why the others are wrong
Step 1: Option A
A z-test requires $σ$ to be known; here it is not, so this is incorrect.
Step 2: Option C
A two-sample t-test compares two independent groups, but there is only one sample here.
Step 3: Option D
A paired t-test requires two related measurements per subject; there is no pairing described.
Step 4: Select correct answer
The one-sample t-test is correct since $σ$ is unknown.
Question 2
Which statement about Type I and Type II errors is correct?
No clue? Show me the answer
Correct answerCorrect!Incorrect
BA Type I error is rejecting a true $H_{0}$

Free preview

AHL 4.18—T and Z test, type I and II errors

Step-by-step walkthrough

Step 1: Identify what is known

Step 2: Apply the decision rule

Step 3: Check sample structure

Step 4: Conclude

Step 1: Option A

Step 2: Option C

Step 3: Option D

Step 4: Select correct answer

14 more questions in this topic

AHL 4.18—T and Z test, type I and II errors

Step-by-step walkthrough

Step 1: Identify what is known

Step 2: Apply the decision rule

Step 3: Check sample structure

Step 4: Conclude

Step 1: Option A

Step 2: Option C

Step 3: Option D

Step 4: Select correct answer

14 more questions in this topic