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All euros have a national image on the \"heads\" side and a common design on the

ID: 3322158 • Letter: A

Question

All euros have a national image on the "heads" side and a common design on the "tails" side. Spinning a coin, unlike tossing it, may not give heads and tails with equal probabilities. Polish students spun the Belgian euro 290 times, with its portly king, Albert, displayed on the heads side. The result was 170 heads. How significant is this evidence against equal probabilities? Follow the four-step process. (Round your test statistic to two decimal places and your P-value to four decimal places. Assume a 95% confidence level.) P-value = Conclusion There is significant evidence that the proportion of times a Belgian Euro coin spins heads is not 0.50 There is not enough evidence to conclude that the proportion of times a Belgian Euro coin spins heads is not 0.50

Explanation / Answer

Given that,
possibile chances (x)=170
sample size(n)=290
success rate ( p )= x/n = 0.5862
success probability,( po )=0.5
failure probability,( qo) = 0.5
null, Ho:p=0.5  
alternate, H1: p!=0.5
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.58621-0.5/(sqrt(0.25)/290)
zo =2.9361
| zo | =2.9361
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =2.936 & | z | =1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.9361 ) = 0.00332
hence value of p0.05 > 0.0033,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.5
alternate, H1: p!=0.5
test statistic: 2.9361
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.00332

there is significant to conclude that the proportion of times a belgian euro coin spins heads is not 0.50

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