A machine is supposed to produce random digits. Bob thinks that the machine is not fair and that the probability of it producing the digit 0 is less than $$$\frac{1}{10}$$$. In order to test his suspicion he notes the number of times the digit 0 occurs in 30 digits produced by the machine. He carries out a test at the $$$10 \%$$$ significance level.

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_62 Year：2021 Question No：6(a)

Answer:

$\mathrm{H}_{0}: \mathrm{P}(0)=\frac{1}{10}$
$\mathrm{H}_{1}: \mathrm{P}(0)<\frac{1}{10}$

Knowledge points:

6.5.1 understand the nature of a hypothesis test, the difference between one-tailed and two-tailed tests, and the terms null hypothesis, alternative hypothesis, significance level, rejection region (or critical region), acceptance region and test statistic (Outcomes of hypothesis tests are expected to be interpreted in terms of the contexts in which questions are set.)

6.5.2.1 direct evaluation of probabilities

6.5.2.2 a normal approximation to the binomial or the Poisson distribution, where appropriate

Answer:

Knowledge points:

Solution:

Related Question