Question

In 2008, Devry “University” infamously collected data comparing the starting salaries of graduating students with surnames beginning with the letters A through M with those whose surnames begin with N through Z. The study was famously panned. For a sample of 30 students in the A-M category, the avg starting salary was $37,233.33, with a standard deviation of $3475.54. For a sample of 36 students with surnames beginning with N-Z, the average starting salary was $35855.81, with a standard deviation of $2580.02. Test to see in the populations are actually equal using a 2% significance level.

Answer 1

To test to see in the populations are actually equal using a 2% significance level,

we conduct a hypothesis test to see if the population means are equal or not

	n	Mean (M)	Variance (SS)	Standard Deviation (SD)
X	n1 = 30	M1 = 37233.33	SS1 = 12079378.2916	s1 = 3475.54
Y	n2 = 36	M2 = 35855.81	SS2 = 6656503.2004	s2 = 2580.02

The null and alternative hypotheses are
Ho :  μ1 = μ2           (Populations are equal)
Ha :  μ1 ≠ μ2           (Populations are not equal)
where μ1, μ2 are population means for starting salaries of the two categories (surnames A-M and N-Z) respectively.
α = 0.02                 2% level of significance.

We use independent Samples T test since population standard deviation is unknown.

Using the given formulae, we get

Degrees of Freedom
df1 = n1 - 1 , df2 = n2 - 1 , df = n1 + n2 - 2 = 30 + 36 - 2 = 64

df = 64

Pooled Variance

Sp² = 9113743.4761

Mean Squared Error S_m1-m2

S_m1-m2 = 746.2915

t-statistic

t-statistic = t = 1.8458


P-value
For t = 1.8458, df = 64 we find the two tailed p-value using t tables or Excel function t.dist.2t
p-value = t.dist.2t(abs(1.8458), 64)
p-value = 0.0695


Decision
0.0695 > 0.02
that is p-value is greater than α.
Hence we DO NOT Reject Ho.

Conclusion
There does not exist enough statistical evidence at α = 0.02 to show that the samples are from different populations.

In other words,

The populations are actually equal.