Word Usage and Gender Mahl 2009 reported in the journal the

(Word Usage and Gender) Mahl (2009) reported in the journal the results of an extensive study of 396 men and women, comparing the number of words uttered per day by each sex. Volunteer participants wore inconspicuous recording devices that recorded the subjects\' daily word usage. Is there any validity to the notion that women talk more than men do? The following fictional data produce results similar to those obtained by Mahl (2009). Assume = .05 with a one-tail hypothesis in the direction described above.

Table: Word Usage and Gender

Women

Men

17,214

16,322

15,325

14,636

14,022

17,045

18,643

18,873

15,800

13,071

(a) What type of statistical analysis should be run to address this question?

(b) What are the assumptions of your chosen statistical test?

(c) Identify the null and alternative/research hypotheses in both words and symbols.

(d) Calculate the test statistic that will help you answer this question

(e) Identify the critical value(s) for your statistical test.

(f) Draw conclusion regarding the null hypothesis and the subject matter.

(g) Write the statistical information from your test in APA format.

Solution

a)
t Test of Difference Means for Unequal Variance
b)
we assume that distribution is normal
c)
Set Up Hypothesis
Null, men talk more OR equal perform as like wommen do Ho: u1 < u2
Alternate, women talk more than men do - H1: u1 > u2
d)
Test Statistic
X(Mean)=16200.8
Standard Deviation(s.d1)=1779.449 ; Number(n1)=5
Y(Mean)=15989.4
Standard Deviation(s.d2)=2229.844; Number(n2)=5
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =16200.8-15989.4/Sqrt((3166438.7436/5)+(4972204.26434/5))
to =0.17
| to | =0.17
e)
Critical Value
The Value of |t a| with Min (n1-1, n2-1) i.e 4 d.f is 2.132
We got |to| = 0.1657 & | t a | = 2.132
f)
Make Decision
Hence Value of |to | < | t a | and Here we Do not Reject Ho
P-Value:Right Tail -Ha : ( P > 0.1657 ) = 0.43822
Hence Value of P0.05 < 0.43822,Here We Do not Reject Ho

g)

men talk more OR equal perform as like wommen do