Question

Your friend thinks that men and women get tipped differently. Say in a sample of 8 men, they have an average of $45 in tips with a standard deviation of 2. In a sample of 7 women, they have an average of $39 in tips with a standard deviation of 5. is there evidence that men and women get tipped differently?

Answer 1

H₀:

H1:

The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

= (45 - 39)/sqrt(2^2/8 + 5^2/7)

= 2.97

Df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

= (2^2/8 + 5^2/7)^2/((2^2/8)^2/7 + (5^2/7)^2/6)

= 8

At alpha = 0.05, the critical value is t_{0.025, 8} = +/- 2.306

Since the test statistic value is greater than the positive critical value (2.97 > 2.306), so we should reject the null hypothesis.

There is sufficient evidence to conclude that men and women get tipped differently.