Question

According to a recent survey of 1700 people, 63% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Required:
Which distribution should you use for this problem?

Answer 1

The standard normal distribution should be used due to the large sample size ; also also proportions are what is required.

Explanation:

Given that:

Sample size, n = 1700

p = 63% = 0.63

Given that the sample size is large at n = 1700 ; the binomial distribution and t - distribution aren't ideal for distributions of such size. Also, we are interested in the population proportion which from the standard normal formula who's interval could be obtained thus :

[p ± Zα/2 * sqrt(p(1 - p))]

Both the t-distributon and binomial distributions are for experiments whith relatively small or low.