Significant Difference?

Date: 05/08/99 at 20:34:32
From: Rita
Subject: Statistics problem

Dear Dr. Math,

I have the following problem that I can't understand:

The following data come from a study of delivery times for babies in a 
large NYC hospital. The research question was: 

Does mean delivery time differ for boy babies and girl babies?

                    girls         boys
     mean           685.8        750.6
     st.dev         428.0        448.0
     N               76           54

Delivery time is in minutes.

a) State the null hypothesis in words and symbols.
b) Perform a t-test by hand, using either the confidence interval
   or critical value approach.
c) Do you reject or fail to reject H0? Justify your answer.
d) What is your conclusion with respect to the research question?
e) Does it matter whether delivery time is normally distributed?
   Justify your answer.

Thank you for answering my question!

Rita

Date: 05/09/99 at 06:53:16
From: Doctor Anthony
Subject: Re: Statistics problem


a) State the null hypothesis in words and symbols.

The null hypothesis is that the means are the same

   If m = difference in sample means, then H0 is m=0

b) Perform a t-test by hand, using either the confidence interval
   or critical value approach.

   m = 750.6 -685.8 =  64.8

                                      n1.s1^2 + n2.s2^2
We assume a common variance given by  -------------------
                                        n1 + n2 - 2

      76 x 428^2 + 54 x 448^2
   =  -----------------------  = 193437.5     s.d. = 439.8
           76 + 54 - 2

              64.8 - 0                 64.8
   t = -----------------------  =   ----------  =  0.827
       439.8 sqrt(1/76 + 1/54)         78.275


Degrees of freedom = 76 + 54 - 2 = 128

The tabular t value for a 5% significance level is 1.66, so our value 
of 

   t = 0.827 is NOT significant


c) Do you reject or fail to reject H0? Justify your answer.

We do NOT reject the null hypothesis. The t-value is well below the 
significance level even at 25%.

d) What is your conclusion with respect to the research question?

There is no significant difference between boys and girls. The reason 
is the VERY LARGE standard deviation of the two populations.
 
e) Does it matter whether delivery time is normally distributed?

No it does not matter because by the central limit theorem the 
distribution of means of samples is approximately normal even if the 
underlying distribution is not Normal.

- Doctor Anthony, The Math Forum
  http://mathforum.org/dr.math/