Question

Please complete the following questions with detailed steps and explanations.

Historically, 15% of students at a university undertake an internship during the summer break. A university claims that the number of students who took up summer internships reached a record high in 2015. A sample of 400 students reveals that 120 were working as interns in the summer of 2015. Use a 1% significance level to determine if there is any evidence that the proportion of students in internship positions was higher in 2015 than historically?

Answer 1

Here we have,

number of students randomly selected from university = n =400,

number of students working as interns = x = 120 ,

Level of significance = = 0.01 ,

Claim : The proportion of students in internship positions was higher in 2015 than historically.

The hypothesis are :

H0 : P = 0.15 v/s H1 : P > 0.15 ( claim )

The test statistic is,

  

= -6.55

The critical value is,

The critical region is , area above critical value 2.33.

Here calculated value of z do not lie in the critical region. Hence we failed to reject null hypothesis.

Conclusion : There are no sufficient evidence to support the claim that the proportion of students in internship positions was higher in 2015 than historically.