A human resources consultant to a large company claims that

A human resources consultant to a large company claims that at most 40% of managers are dissatisfied with office politics. A random sample of 200 managers had 90 who expressed dissatisfaction with office politics. The p-value for this test of hypothesis is ____________ and the correct conclusion is __________ at the 10% level of significance.

a).0749; Reject Ho

b).0749; Fail to reject Ho

c).0778; Reject Ho

d).0778; Fail to reject Ho

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.4
Ha:   p   <   0.4
As we see, the hypothesized po =   0.4      
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] =    0.034641016      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.443375673      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.0749      

significance level =    0.1      

Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.      

Thus,

OPTION A: 0.0749, Reject Ho. [ANSWER]