Research at the University of Toledo indicates that 30 percent of students chang

Question

Research at the University of Toledo indicates that 30 percent of students change their major area of study after their first year in a program. A random sample of 100 students in the College of Business revealed that 25 had changed their major area of study after their first year of the program. Estimate the proportion of students who change their major after the first year in this program with 95% confidence. As part of your work, show that the conditions for the large-sample CI are met. Include a statement of interpretation of the interval. Fill in the blanks below to report your answers: We are blank #1 confident that the proportion of students who change their major after the first year in the program is between blank #2 (as % to nearest tenth) and blank =3 (as % to nearest tenth). Blank #1 __________ Blank #2 ___________ Blank #3 ___________

Explanation / Answer

Given :

Population proportion P = 30% or 0.30

Sample Proportion P^ = 25/100 = 0.25

Sample size = 100

Confidence level = 0.95 or 95%

.

The formula of confidence interval is

P^ - Z * SE , P^ + Z*SE

.

SE = P^*(1-P^)/n

SE = (0.25 * 0.75 /100)

SE = 0.0433

.

P^ = 0.25

Z for 95% confidence level is 1.96

.

On plugging these values we get:

0.25 - 1.96 *0.0433 , 0.25 +1.96 * 0.0433

0.25 - 0.0849 , 0.25 + 0.0849

0.1651 , 0.3349

.

Thus we are 95% confident that the proportion of students who change their major after the first year in the program is between 16.5% and 33.5%.

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