All euros have a national image on the heads side and a comm

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 246 times, with its portly king, Albert, displayed on the heads side. The result was 124 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:

or

choose one between rejected or not rejected.

Solution

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 =    0.504065041      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.031878836      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    0.127515343   [ANSWER]  
**************************************          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.898532531 [ANSWER]

********************************************      
significance level =    0.02      

Comparing p >0.02, we   FAIL TO REJECT THE NULL HYPOTHESIS. [NOT REJECTED]