Question

50% 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 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the proportion of students who change their major after the first year in this program

Answer 1

Hence, since z ( - 0.4 ) is greater than ( -1.65 );

we reject H₀, Null hypothesis,

Therefore, There is no evidence that there has been a significance decrease in the proportion of students who change their major after the first year in the program.

Explanation:

Given the data in the question;

Let p = 50% = 0.5

Hypothesis;

Null hypothesis H₀ : p ≥ 0.5

Alternative hypothesis H₁ : p < 0.5

x = 48

sample size n = 100

sample proportion p" = x / n = 48 / 100 = 0.48

significance value = 0.5

`Z_\alpha` = -1.65

Test Statistics;

z = (p" - p) / √( p( 1 - p ) / n )

we substitute

z = (0.48 - 0.5) / √( 0.5( 1 - 0.5 ) / 100)

z = -0.02 / √( 0.25 / 100 )

z = -0.02 / √0.0025

z = -0.02 / 0.05

z = -0.4

Hence, since z ( - 0.4 ) is greater than ( -1.65 );

we reject H₀, Null hypothesis,

Therefore, There is no evidence that there has been a significance decrease in the proportion of students who change their major after the first year in the program