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

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 264 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 = 0.04.

z-stat = _____

with pvalue of ____

nully hypothesis is rejected or not rejected

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.534090909      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.030772873      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.107823419   [ANSWER, Z STAT]

********************************  
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.267938084   [ANSWER, P VALUE]

*********************************  

As P > 0.04, we   FAIL TO REJECT THE NULL HYPOTHESIS.   [NOT REJECTED, ANSWER]  

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