What does the one-tailed test at the 5% level…

What does the one-tailed test at the 5% level conclude about the coaching centre's claim?

Question 50

MediumOriginal question

A coaching centre claims its students score more than 70 on average in a mock test. A random sample of 25 of its students has a mean of 74 with standard deviation 10. For 24 degrees of freedom at the 5% level, the one-tailed critical value of $t$ is 1.711 and the two-tailed one is 2.064.

What does the one-tailed test at the 5% level conclude about the coaching centre's claim?

Do not reject

H_0

t = 2

is below 2.064Correct answerYour answerReject

H_0

t = 2

is above 1.711, so the data back the claimCorrect answerYour answerReject the claim: the sample mean is only 4 marks above 70Correct answerYour answerProve that every student scores above 70Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

A right-tailed test compares $t$ with the one-tailed critical value, 1.711.
$2 > 1.711$ : reject $H_0$ and accept that the mean is above 70.

Worth noting

2.064 is the two-tailed value; a claim of 'more than' needs only one tail.

Concept: Deciding a one-tailed test
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsNull and alternate hypotheses

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 does the one-tailed test at the 5% level conclude about the coaching centre's claim?

Question 50

Explanation