Question

You are applying for a student Job at IMC and are challenging the salary of 400 EUR per month as you think it is too low. During negotiations the HR manager assured you that all students’ salaries are at 400 EUR +/- 5%.

As you are a statistics student, you want to make a survey to find out if what the lady claimed is true or if your hunch that it is higher than 400 EUR is true. You make a quick online survey inviting all students of IMC. One of the questions is whether they are working or have worked in the last 12 months on a comparable student job at IMC and if they answered yes, you asked what their exact monthly salary was. You so gathered 81 valid answers and calculated the mean of the given salaries, which is 420 EUR with a stdev of 90 EUR.

a) What would be the Null Hypothesis H0 and what would be the alternative Hypothesis H1?

b) Which significance level would you use and why?

c) What is your conclusion/inference? Were you treated fairly?

Answer 1

a) What would be the Null Hypothesis H0 and what would be the alternative Hypothesis H1?

The null hypothesis, H₀: µ = 400

The alternative hypothesis, H₁: µ > 400

b) Which significance level would you use and why?

The significance level should be 0.05 to see if all students’ salaries are at 400 EUR +/- 5%.

c) What is your conclusion/inference? Were you treated fairly?

The output is:

400.00	hypothesized value
420.00	mean Students’ salaries
90.00	std. dev.
10.00	std. error
81	n
80	df
2.000	t
.0244	p-value (one-tailed, upper)

Since the p-value (0.0244) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that all students’ salaries are higher than 400 EUR is true.