Question

A random sample of graduated students from Acsenda is taken to identify how much of students find job after their graduation. 348 out of 400 students had a satisfying job. The management has concluded that 90% of graduated students have found a satisfying job. Test the hypothesis at 0.05 level of significance to see if the management is correct.

Answer 1

The sample proportion here is computed as:

p = x/n = 348/400 = 0.87

The test statistic now is computed here as:

As we are testing here whether the proportion of graduate students that have found a specifying job is less than 0.9, therefore the p-value here is computed from the standard normal tables as:
p = P(Z < -2) = 0.0228

As the p-value here is 0.0228 < 0.05 which is the level of significance, therefore the test is significant and we can reject the management's claim that  90% of graduated students have found a satisfying job