Quick questions on Hypothesis testing for a mean: VCE Specialist Mathematics Unit 4

Q: What are hypotheses?

Overfilling means a mean above 500, so

Q: What is decision?

Since p = 0.0668 > α = 0.05, we do not reject H_0. There is insufficient evidence at the 5\% level to conclude the machine overfills.

Q: What is q1?

Write H_0 and a two-tailed H_1 for testing whether a mean equals 20. [2 marks]

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are hypotheses?

Show answer

Overfilling means a mean above

500

, so

What is decision?

Show answer

Since

p = 0.0668 > \alpha = 0.05

, we do not reject

H_0

. There is insufficient evidence at the

5\%

level to conclude the machine overfills.

What is q1?

Show answer

Write

H_0

and a two-tailed

H_1

for testing whether a mean equals

20

. [2 marks]

What is q2?

Show answer

Compute the test statistic for

\bar{x} = 27

\mu_0 = 25

\sigma = 6

n = 36

. [2 marks]

What is q3?

Show answer

Define a Type I error. [1 mark]

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