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 247 times, with its portly king, Albert, displayed on the heads side. The result was 132 heads.

Test the hypothesis that the proportion of times a Belgian Euro coin spins heads equals 50% at alpha = 0.01 .

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

The null hypothesis is:

rejected

not rejected

Answer 1

Solution :

Given that,

= 0.50

1 - = 0.50

n = 247

x = 132

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.534

This a two tailed test.

A)

Ho: p = 0.50

Ha: p 0.50

Test statistics

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

= ( 0.534 - 0.50) / (0.50*0.50) / 247

= 1.069

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

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

=2*( 1- P(Z < 1.069))

= 2*(1 - 0.8575)

= 2*0.1425

= 0.285

The p-value is p = 0.285, and since p = 0.285 >0.01, it is concluded that the null hypothesis is not rejected.