Has the recent drop in airline passengers resulted in better on-time performance

Question

Has the recent drop in airline passengers resulted in better on-time performance? Before the recent downturn, one airline bragged that 92% of its flights were on time. A random sample of 165 flights completed this year reveals that 153 were on time. We desire to find if the airline's on-time performance has improved  (HA:p>0.92).

Suppose the critical point was p^*=0.94p^*=0.94 (it is not but this is the number given to use), if the actual on-time proportion for the flights has increased to 95%, what is the power of the test?

Please write out any and all steps you took, I don't understand power at all. I also use a TI-84 Plus, if you (the expert) also use one and used any functions that come on it. This is part of an ungraded review question for a midterm. The answer to this problem is given and is 0.7221, but I want to know how to find it myself.

Explanation / Answer

here as true proportion p=0.95

therefore for sample size n=165 ; standard errror of proportion =SEp =(p*(1-p)/n)1/2 =0.0170

hence power of the test =P(rejecting null hypothesis)=P(X>0.94)=P(Z>(0.94-0.95)/0.0170)

=P(Z>-0.5882)=1-P(Z<-0.5882) =1-0.2779 =~0.7221

( please revert for any clarification required)

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