A sample of 16 bags has mean weight 104 g and standard deviation 8 g. Testing H₀: μ = 100 against H₁: μ ≠ 100 at the 5% level, with critical value t = 2.131 for 15 degrees of freedom, what is the decision?

Do not reject H₀: the data fit the claim

Reject H₀: the mean differs from the claim

Reject H₀ because t is positive

Accept H₁ because the sample mean is not equal to the claim

Question 69

HardOriginal question

A sample of 16 bags has mean weight 104 g and standard deviation 8 g. Testing $H_0: \mu = 100$ against $H_1: \mu \ne 100$ at the 5% level, with critical value $t = 2.131$ for 15 degrees of freedom, what is the decision?

Reject

H_0

: the mean differs from the claimCorrect answerYour answerReject

H_0

because

t

is positiveCorrect answerYour answerAccept

H_1

because the sample mean is not equal to the claimCorrect answerYour answerDo not reject

H_0

: the data fit the claimCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$t = \frac{104 - 100}{8/\sqrt{16}} = \frac{4}{2} = 2$ .
$\lvert t \rvert = 2 < 2.131$ , so the difference could be chance: do not reject $H_0$ .

Worth noting

A sample mean different from 100 is not enough by itself; it must be far enough, beyond the critical value.

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