Assume that someone claims they can predict if the coin lands heads or tails up
ID: 2928868 • Letter: A
Question
Assume that someone claims they can predict if the coin lands heads or tails up based only on the sound of the coin (not looking at the coin). You want to check this claim and conduct the experiment: the coin is flipped n times, and the "magician" tries to predict the outcome.
(a) State the hypothesis for this problem and, assuming that n = 10, find the test with significance level 0.1 (think carefully about the alternative hypothesis).
(b) Find the (approximate) probability of type II error against the alternative that the "magician" can predict the outcome based on the sound with probability 0.75.
(c) Assume that the "magician" guessed 7 out of 10 coins correctly. What is the associated p-value of your test?
(d) What is the minimal number of coins throws necessary to obtain the test with significance level 0.1 and power 0.9 (for the alternative hypothesis as in the previous question)?
Explanation / Answer
Given that,
possibile chances (x)=7
sample size(n)=10
success rate ( p )= x/n = 0.7
success probability,( po )=0.5
failure probability,( qo) = 0.5
null, Ho:p=0.5
alternate, H1: p!=0.5
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.64
since our test is two-tailed
reject Ho, if zo < -1.64 OR if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.7-0.5/(sqrt(0.25)/10)
zo =1.2649
| zo | =1.2649
critical value
the value of |z | at los 0.1% is 1.64
we got |zo| =1.265 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.26491 ) = 0.2059
hence value of p0.1 < 0.2059,here we do not reject Ho
ANSWERS
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null, Ho:p=0.5
alternate, H1: p!=0.5
test statistic: 1.2649
critical value: -1.64 , 1.64
decision: do not reject Ho
p-value: 0.2059
we do not have enough evidence to support he claim