A larger sample of 64 bulbs gives the same…

A larger sample of 64 bulbs gives the same mean of 960 hours and standard deviation of 80 hours.

Question 70

HardOriginal 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.

A larger sample of 64 bulbs gives the same mean of 960 hours and standard deviation of 80 hours. What is the $t$ -value now?

-4

Correct answerYour answer

-3

Correct answerYour answer

-2

Correct answerYour answer

-1

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Standard error $= \frac{80}{\sqrt{64}} = 10$ .
$t = \frac{-40}{10} = -4$ : the same gap is now much harder to put down to chance.

Worth noting

$-8$ divides by $\frac{80}{16}$ , using $\sqrt{n} = 16$ for $n = 64$ ; $\sqrt{64} = 8$ .

Concept: Larger samples sharpen a test
Typical timeTypical: 150 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.

A larger sample of 64 bulbs gives the same mean of 960 hours and standard deviation of 80 hours.

Question 70

Explanation