Question

HW 20

A researcher wants to know if students are more successful in taking online courses now as compared to 2016. In 2016, 44% of students taking an online class passed the class. She collects data from 125 online students, and finds that 58 of them passed their classes . Test her claim that the percentage of successful completion has increased since 2016.

*What is the null hypothesis?                            [ Select ]                       ["HA: mu>0.44", "H0: p=44", "H0: mu=44", "H0: p=0.44", "H0: mu=0.44"]      

*What is the alternative hypothesis?                            [ Select ]                       ["HA: mu < 0.44", "HA: P < 0.44", "HA: p > 0.44", "H0: mu is not equal to 0.44"]      

*This test is                            [ Select ]                       ["right tailed", "left tailed", "two tailed"]      

*Which distribution and what degrees of freedom do you need?                            [ Select ]                       ["The normal distribution with 124 degrees of freedom.", "The normal distribution", "The student t-distribution with 124 degrees of freedom.", "The student t-distribution with 125 degrees of freedom."]      

*The test statistic is                            [ Select ]                       ["0.5406", "0.464", "0.0444", "1.96", "0.2944"]      

*The P-value is                            [ Select ]                       ["0.2944", "0.464", "0.0444", "0.5406", "0.048"]      

*What is the conclusion?                             [ Select ]                       ["Reject the null hypothesis. Evidence supports the claim that the percent of successful students is higher than in 2016.", "Fail to reject the null hypothesis. There is insufficient evidence to conclude that the percent of successful students is higher than in 2016.", "Reject the null hypothesis. There is insufficient evidence to conclude that the percent of successful students is higher than in 2016.", "Fail to reject the null hypothesis. Evidence supports the claim that the percent of successful students is higher than in 2016."]      

Answer 1

Solution:
Given in the question
The claim is that the percentage of successful completion has increased from 44% since 2016 so null and alternate hypothesis can be written as
Null hypothesis H0: p = 0.44
Alternate hypothesis Ha: p > 0.44
Number of sample = 125
Number of favourable cases = 58
Sample proportion p^ = 58/125 = 0.464
Here we will use One proportion Z test or standard normal distribution as
np = 125*0.44 = 55 >5
n*(1-p) = 125*(1-0.44) = 70>5
As we can see both np and n(1-p) are greater than 5, So test statistic can be calculated as
Test stat = (p^ - p)/sqrt(p*(1-p)/n) = (0.464 - 0.44)/sqrt(0.44*(1-0.44)/125) = 0.5406
As this is right tailed test so from Z table we found p-value = 0.2944
At alpha = 0.05, we are failed to reject the null hypothesis as p-value is greater than alpha value (0.2944>0.05)
So Fail to reject the null hypothesis. There is insufficient evidence to conclude that the percent of successful students is higher than in 2016.