If the coaching centre's claim had been tested…

If the coaching centre's claim had been tested two-tailed at the 5% level, what would the conclusion be?

Question 51

HardOriginal 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.

If the coaching centre's claim had been tested two-tailed at the 5% level, what would the conclusion be?

Reject

H_0

, since

t = 2

is above 1.711Correct answerYour answerThe same conclusion as the one-tailed testCorrect answerYour answerReject

H_0

, since a two-tailed test is stricter about the meanCorrect answerYour answerDo not reject

H_0

, since

t = 2

is below 2.064Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Two-tailed, the 5% is split between both tails, so the critical value rises to 2.064.
$t = 2 < 2.064$ : do not reject $H_0$ . The choice of tails can change the verdict.

Worth noting

1.711 is the one-tailed value; it does not apply to a two-tailed test.

Concept: One tail or two
Typical timeTypical: 150 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.

If the coaching centre's claim had been tested two-tailed at the 5% level, what would the conclusion be?

Question 51

Explanation