Question

) It has been estimated that 53% of all college students change their major at least once during the course of their college career. Suppose you are told that the sample proportion for a random sample was 0.48. Furthermore, you are told that the probability of geing a sample proportion of this size or smaller is 14%. What must have been the sample size?

Answer 1

Answer:

116 students

Step-by-step explanation:

The standard deviation for a proportion is:

$s=\sqrt{\frac{(1-p)*p}{n}}$

For any measured sample proportion x, the z score is given by:

$z = \frac{x-p}{s}$

The population proportion is 0.53

At the 14th percentile, the corresponding z-score is z =-1.08.

Since 0.48 is at the 14th percentile, the standard deviation is:

$-1.08=\frac{0.48-0.53}{s}\\ s=0.46296$

Therefore, the sample size 'n' is given by:

$0.046296=\sqrt{\frac{(1-0.53)*0.53}{n}}\\n=\frac{0.47*0.53}{0.046296^2}\\n= 116\ students$

The sample size must have been of 116 students.