Research at the university of toledo indicates that 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? test at the 0.05 level of significance.

So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to  FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students that had changed their major area of study after their first year of the program is not significantly less than 0.5 or 50%.

Step-by-step explanation:

1) Data given and notation

n=100 represent the random sample taken

X=48 represent the students that had changed their major area of study after their first year of the program

estimated proportion of students that had changed their major area of study after their first year of the program

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that if we have a significant decrease in the proportion of students who change their major after the first year in this program.:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided . The next step would be calculate the p value for this test.  

Since is a left taild test the p value would be:  

So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to  FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students that had changed their major area of study after their first year of the program is not significantly less than 0.5 or 50%.

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step-by-step explanation: