In 1999 Todd\'s housemate, Steve is trying to convince Todd to get a Palm Pilot

Question

In 1999 Todd's housemate, Steve is trying to convince Todd to get a Palm Pilot (think iPhone's great-grandfather). Todd is sensitive to popular opinion and will only get one when "everyone else is doing It Todd and Steve agree that if Steve can show greater than 60% of the people at UD have one then Todd will get one. Steve immediately takes a sample of 60 people from the 2nd floor North at Stuart Hall. The sample revealed 44 people who had a Palm Pilot. a. Will Todd get a Palm Pilot? Test the hypothesis H_o: probability = 0.6 H_a: probability > 0.6 b. Do you have any concerns about the sample that was taken?

Explanation / Answer

a)null hypothesis: p<=0.6

alternate hypothesis: p>0.6

std error=(p(1-p)/n)1/2 where p=0.6 and n=60

=0.063

point estimate phat=44/60=0.733

hence test stat z=(phat-p)/std error =(0.733-0.6)/0.063=2.103

for above p value =0.0177

as p value is ;less then 0.05 ; we can reject null hypothesis and therefore Todd should get a palm pilot

b) as above sample is taken from a specific place and hence can not be termed as random; therefore it does not represent the population.

From above it may overestimate the proportion

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