A national survey shows that $$$95 \%$$$ of year 12 students use social media. Arvin suspects that the percentage of year 12 students at his college who use social media is less than the national percentage. He chooses a random sample of 20 students at his college and notes the number who use social media. He then carries out a test at the $$$2 \%$$$ significance level. Jimmy believes that the true percentage at Arvin's college is $$$70 \%$$$. Assuming that Jimmy is correct, find the probability of a Type II error. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m20_qp_62 Year：2020 Question No：7(c)

Answer:

Use of $B(20,0.7)$
$\mathrm{P}(X>16 \mid p=0.7)$
$=0.107$

Knowledge points:

6.5.5 calculate the probabilities of making Type I and Type II errors in specific situations involving tests based on a normal distribution or direct evaluation of binomial or Poisson probabilities.

Answer:

Knowledge points:

Solution:

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