Need help with question 43 part A 43 A plan for an executive

Need help with question 43 part A 43. A plan for an executive travelers^? club has been developed by an airline on the premise that 5% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who would qualify. a. Using this data, test at level .01 the null hypothesis that the company^?s premise is correct against the alternative that it is not correct. b. What is the probability that when the test of part (a) is used, the company^?s premise will be judged correct when in fact 10% of all current customers qualify? 44. Each of a group of 20 intermediate tennis players is given two rackets, one having nylon strings and the other synthetic

Solution

A.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.05
Ha:   p   =/=   0.05
As we see, the hypothesized po =   0.05      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.08      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.009746794      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    3.077935056      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.001042202      
significance level =    0.01      
Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.      

Thus, there is sufficient evidence that the proportion of those who qualify is not 5% (it is actually greater than that).

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