Question

The Australian Bureau of Statistics (ABS) has collected data on the part-time employment patterns of full-time male students in Australia and found that they worked 16 hours per week on average. A researcher believes that female students may work fewer hours on average than male students. Accordingly, she selects 36 female students at random and finds the average number of hours worked per week to be 13.5 and the standard deviation is 7 hours. To see if her belief is substantiated, conduct the appropriate test at a significance level of 5% and interpret the result. State the assumptions made.

Answer 1

ho: female students may work equal hours on average as compared to male students. u = 16
h1: female students may work fewer hours on average than male students. u < 16

critical value, -z(a) = -z(0.05)
-z(a) = -1.645

test statistic, z = (mean-u)/(sd/sqrt(n))
z = (13.5-16)/(7/sqrt(36))
z = -2.1429

p-value, P(Z<z) = P(z<-2.1429)
P(Z<z) = NORMSDIST(-2.1429)
P(Z<z) = 0.016060564

With (z = -2.14, p<5%), i reject Ho and conclude that female students may work fewer hours on average than male students. u < 16