What should be concluded about the bulb…

What should be concluded about the bulb maker's claim at the 5% level?

Question 63

MediumOriginal question

A bulb maker claims its bulbs last 1,000 hours on average. A sample of 16 bulbs lasts a mean of 960 hours with standard deviation 80 hours. At the 5% level, the two-tailed critical value of $t$ for 15 degrees of freedom is 2.131.

What should be concluded about the bulb maker's claim at the 5% level?

Reject

H_0

: the sample mean is 40 hours shortCorrect answerYour answerDo not reject

H_0

|t| = 2

is less than 2.131Correct answerYour answerReject

H_0

t

is negativeCorrect answerYour answerAccept that the true mean is 960 hoursCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$|t| = 2$ and the critical value is 2.131.
$2 < 2.131$ , so the shortfall could be chance: do not reject the claim.

Worth noting

A sample mean below the claim is not enough by itself; the test asks whether the gap is bigger than chance allows.

Concept: Comparing $|t|$ with the critical value
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe one-sample t-test

Practise this chapter →

Ten questions from Sampling, Inference & the t-Test, at your own pace.

Practise this chapter →

Ten questions from Sampling, Inference & the t-Test, at your own pace.

What should be concluded about the bulb maker's claim at the 5% level?

Question 63

Explanation