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 237 times, with its portly king, Albert, displayed on the heads side. The result was 152 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:

not rejected

rejected

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

= x / n = 152 / 237 = 0.6414

P₀ = 0.5

1 - P₀ = 0.5

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.6414 - 0.5 / [(0.5 * 0.5) / 237]

= 4.35

P(z > 4.35) = 1 - P(z < 4.35) = 0

P-value = 0

= 0.02

P-value <

Reject the null hypothesis .