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 235 times, with its portly king, Albert, displayed on the heads side. The result was 141 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 = 235

x = 141

Level of significance = = 0.02

Point estimate = sample proportion = = x / n = 0.6

This a two tailed test.

The null and alternative hypothesis is,

Ho: p = 0.50

Ha: p 0.50

Test statistics

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

= ( 0.6 - 0.50) / (0.50*0.50) / 235

= 3.066

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

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

= 2*(1- P(Z < 3.066))

= 2*(1 - 0.9989)

= 2*0.0011

= 0.002

The p-value is p = 0.002, and since p = 0.002 < 0.02, it is concluded that the null hypothesis is rejected.