Question

A survey of 1010 college seniors working towards an undergraduate degree was conducted. each student was asked, "are you planning or not planning to pursue a graduate degree?" of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. construct and interpret a 98% confidence interval for the proportion of college seniors who are planning to pursue a graduate degree. (0.612, 0.690); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.612 and 0.690. (0.621, 0.680); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.621 and 0.680. (0.616, 0.686); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.616 and 0.686. (0.620, 0.682); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.620 and 0.682.

Answer 1

The confidence interval is (0.616, 0.686).

To find the confidence interval, we first find p, the proportion of students:
658/1010 = 0.6515

The confidence interval follows the formula
$p\pm z(\sqrt{\frac{p(1-p)}{N}})$

To find the z-score associated with this level of confidence:
Convert 98% to a decimal:  98% = 98/100 = 0.98
Subtract from 1:  1-0.98 = 0.02
Divide by 2:  0.02/2 = 0.01
Subtract from 1:  1-0.01 = 0.99

Using a z-table (http://www.z-table.com) we see that this is closer to the z-score 2.33.  

Using our information, we have:
$0.6515\pm 2.33(\sqrt{\frac{0.6515(1-0.6515)}{1010}}) \\ \\0.6515\pm 0.0349$

This gives us the interval (0.6515-0.0349, 0.6515+0.0349) or (0.616, 0.686).