Assume that 60% of patrons in a shopping mall are female, Retired Mr. Johnson co

Question

Assume that 60% of patrons in a shopping mall are female, Retired Mr. Johnson counted 50 patrons passing by him when he was drinking a fresh coffee. He found that only 25 of the patrons he counted was male. Assume this is a random sample and the true percent of male patrons was 40%, was Mr. Johnson's observation very unlikely. Explain y 100 our conclusion: WE WILL use 5% as cutoff level of likelihood. Find the probability that less than or equal 25 male patrons in a sample of 100. a. Yes, indeed it is very unlikely b. No, it is not that unlikely

Explanation / Answer

here expected male in 100 patrons =np=100*0.4=40

and std deviaiton =(np(1-p))1/2 =4.899

threfore probability of having 25 or less number of male patron out of 100 =P(X<=25)=P(Z<(25.5-40)/4.899)

=P(Z<-2.9598)=0.0015

as probability of that happening is less than 0.05 level ; we reject null hypothesis

we have sufficient evidence to conclude that event is indeed more unlikely

option A is correct.

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