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 257 times, with its portly king, Albert, displayed on the heads side. The result was 155 heads.

Test the hypothesis that the proportion of times a Belgian Euro coin spins heads equals 50% at alpha = 0.02 .

The test statistic is z =  with P-value . (Use three decimals on both.)

The null hypothesis is:

Answer 1

Solution :

Given that,

= 0.50

1 - = 0.50

n = 257

x = 155

Level of significance = = 0.02

Point estimate = sample proportion = = x / n = 0.603

This a two tailed test.

Ho: p = 0.50

Ha: p 0.50

Test statistics

z = ( - ) / *(1-) / n

= ( 0.603 - 0.50) / (0.50*0.50) /257

= 3.302

Test statistic is 3.302

P-value = 2*P(Z>z)

= 2*(1 - P(Z <z ))

= 2*(1- P(Z < 3.302))

= 2*(1 - 0.9995)

= 2*0.0005

= 0.001

p-value is 0.001

The p-value is p = 0.001, and since p = 0.001 < 0.02, it is concluded that the null hypothesis is rejected.