Associated Topics || Dr. Math Home || Search Dr. Math

### 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?

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/
```
Associated Topics:
High School Analysis
High School Statistics

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search