Suppose that there are two (2) candidates (i.e., Jones and Johns) in the upcoming presidential election. Sara notes that she has discussed the presidential election candidates with 40 friends, and 27 said that they are voting for candidate Jones. Sara is therefore convinced that candidate Jones will win the election because Jones gets more than 50% of votes.
Question one
No, because she must check that her sample size meets the sufficient conditions for a one-proportion test. She also has to determine if her sample size is large enough. She should conduct a one-proportion z-test.
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Question two
The z-score she obtained is .
As evidenced from
Question three
Given and alpha is given a one-tail test we RN.
Since the p-value is lesser than the alpha value we reject the null hypothesis.
Question four
From calculation, the confidence interval is between 53% and 82%.
As evidenced from
and
Answer should be
Question five
Such a small margin means we are very close to accurately predicting the winner. It however requires quite a large sample for the margin of error to be achieved.
Question six
Simply stated, the number of friends selected may be indicative that you are surrounded by like-minded people and does not necessarily reflect the opinion of the greater population.
References
Zou, K. H., Fielding, J. R., Silverman, S. G., & Tempany, C. M. (2003). Hypothesis testing I: proportions. Radiology , 226 (3), p.611.
