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 2^nd 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_0: probability = 0.6 H_a: probability > 0.6. b. Do you have any concerns about the sample that was taken?

Explanation / Answer

a. Will Todd get a Palm Pilot?

Null HYpothesis : H0 : p = Po = 0.6

Alternative Hypothesis : Ha : p > P0 = 0.6

so it is one directional test

Here p = 44 / 60 = 0.733

standard devaiton of sampling proportion se0 = sqrt [ P0 ( 1- P0)/ N] = sqrt [ 0.6 * 0.4/60] = 0.0632

Test Statistic:

Z = ( p - 0.6)/ seo = (0.733 - 0.6) / 0.0632 = 2.104

The P-Value is 0.017672.The result is significant at p < 0.05.So we can reject the null hypothesis and conclude that probability of public opinion is more than 0.6.

(b) Yes, we have concerns about the sample taken as the sample doesn't represent random population. The sample only belonged to a single floor of a building so can't really represnt an entire population. SO, the randomness assumption is in danger.

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