Question

At a local store, 65 female employees were randomly selected and it was found that their mean monthly income was $647 with a standard deviation of $121.50. Seventy-five male employees were also randomly selected and their mean monthly income was found to be $689 with a standard deviation of $168.70. Test the hypothesis that male employees have a higher monthly income than female employees. Use α = 0.01.

Find the test statistic, t.   

p value

Round to four decimal places.

Answer 1

Given that,
mean(x)=647
standard deviation , S1 =121.5
number(n1)=65
y(mean)=689
standard deviation, S2 =168.70
number(n2)=75
null, Ho: u1 = u2
alternate, H1: μ1 > u2

we use test statistic (t) = (-)/sqrt(sd1^2/n1)+(sd2^2/n2)

t=(647-689)/sqrt((121.5^2/65)+(168.70^2/75)

t=-1.705

#test statistic, t =-1.705

df=n1+n2-

df=65+75-2=138

P-value

P(t138>-1.705)

=0.9548

#P-value=0.9548