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 235 times, with its portly king, Albert, displayed on the heads side. The result was 144 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:

not rejected

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 =    0.612765957      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.032616404      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    3.457338787   [ANSWER, Z]

***********************************  
          
As this is a    2   tailed test, then, getting the p value, by table/technology,  
          
p =    0.000545539   [ANSWER, P VALUE]  

**********************************

As P < 0.01, we   REJECT THE NULL HYPOTHESIS.   [ANSWER: REJECT]  

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