Consider the hypothesis test given by H0p 05 H1 p Solutiona

Consider the hypothesis test given by H_0:p = 0.5 H_1: p

Solution

a)

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 =    0.45      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.05      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1   [answer, test statistic]

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B)

As this is a    left   tailed test, then, getting the left tailed p value of z = -1 using table/technology,
          
p =    0.158655254   [ANSWER, P VALUE]

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c)

significance level =    0.01      

Comparing p > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence to reject Ho. [ANSWER]