Question

A university administrator asserted that upperclassmen spend more time studying than underclassmen. Test this claim against the default that the average number of hours of study per week by the two groups is the same, using the following information based on random samples from each group of students. n LaTeX: \overline{X} X ¯ S Upperclassmen 35 15.6 2.9 Underclassmen 35 12.3 4.1

(a) The value of the test statistic is

(b) The p-value of the test is

(c) The decision of the test, at the 1% significance level, is

Answer 1

Upperclassmen: n1= 35, xbar1= 15.6, s1= 2.9

Underclassmen: n2= 35, xbar2= 12.3 , s2=4.1

Ho : mu1 = mu2 (claim)

H1 : mu1 > mu2

Alpha= 0.01

Df = n1 + n2 - 2= 68

Test statistics

t stat = ( xbar1 - xbar2 ) / sqrt [ ( s1² ÷ n1 ) + ( s2² ÷ n2 ) ]

t stat = 3.888 > t critical = 2.382

We reject Ho

Pvalue = P ( t alpha > t stat ) = 0.00001 < 0.01 = alpha

We reject Ho

There is not sufficient evidence to support claim that the average number of hours of study per week by the two groups is the same