2 Are people in New York taller than people in Indiana Suppo

2. Are people in New York taller than people in Indiana? Suppose we conducted an experiment to find out. We randomly sample 102 New Yorkers and compute a mean height of x¯¯¯1=1.3m, and a standard deviation of s1=0.3m. In addition we randomly sample 84 people from Indiana and compute a mean height of x¯¯¯2=1.1m, and a standard deviation of s2=0.4m.

a) What is the p-value of our dataset under the null hypothesis that says that it is not the case that New Yorkers are taller than people in Indiana, i.e. the average difference in heights =0? Use the largest conservative estimate for the degrees of freedom given in Table D, while choosing the significance level in the Table closest to your t-score.

Using your exact t-score from part a), can we conclude that people from New York are taller than people from Indiana at:

b) The =0.05 significance level?

Yes     No

c) The =0.1 significance level?

Yes     No

Solution

Set Up Hypothesis
Null, Ho: u1 < u2
Alternate, people from New York are taller than people from Indiana - H1: u1 > u2
Test Statistic
X(Mean)=1.3
Standard Deviation(s.d1)=0.3 ; Number(n1)=102
Y(Mean)=1.1
Standard Deviation(s.d2)=0.4; Number(n2)=84
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =1.3-1.1/Sqrt((0.09/102)+(0.16/84))
to =3.7884
| to | =3.7884
AT 0.05 LOS
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 3.7884 ) = 0.00014
Hence Value of P0.05 > 0.00014,Here we Reject Ho

AT 0.01 LOS
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 3.7884 ) = 0.00014
Hence Value of P0.01 > 0.00014,Here we Reject Ho

ANS: AT 0.05 LOS : YES, AT 0.01 LOS : YES