Sibling count data
g1  g0  diff  g1  g0  diff 
14  9  5  4  7  3 
11  12  1  5  5  0 
13  6  7  23  5  18 
7  6  1  15  4  11 
8  3  5  10  12  2 
7  4  3  12  2  10 
4  4  0  3  5  2 
8  5  3  5  6  1 
8  3  5  9  4  5 
6  8  2  4  2  2 
2  7  5  12  4  8 
10  4  6  11  7  4 
11  8  3  9  9  0 
8  9  1  10  5  5 
5  3  2  7  7  0 
6  5  1  5  3  2 
6  13  7  4  6  2 
13  7  6  5  4  1 
10  7  3  2  6  4 
7  7  0  5  8  3 
8  4  4  7  4  3 
2  5  3  10  1  9 
9  7  2  6  5  1 
9  7  2  13  7  6 
10  5  5  10  16  6 
14  5  9    
Quiz 11 Paired ttest for mean difference • Name:
In the table, g0 is the present generation, the number of siblings you have plus yourself.
g1 is your mother (or father's) generation and the number of siblings for one of them plus themself.
This forms 51 pairs of data with a sample mean difference
x_{d} of 2.25 and a sample standard deviation
of the difference s_{d} of 4.67.
This represents a sample mean drop of slightly more than two children in family size.
Run a hypothesis test with a 1% risk of a type I error for whether we have evidence
of a change in family size between your parents generation and your generation.
Do not type in the data in the table! You do not need it. The table is only there so you can see the original data and
satisfy your curiousity on how many children one person might be able to have.
 sample size: n = ______________
 sample mean x_{d} = ______________
 sample standard deviation s_{d} = ______________
 alpha: α = ______________
 degrees of freedom: = ______________
 tcritical: t_{c} = ______________
 tstatistic: t = ______________
 At a 1% risk of rejecting a true null hypothesis:
 ___ Reject the null hypotheis? OR
 ___ Fail to reject the null hypothesis?
 _________ Is the difference in the number of siblings
between the generations statistically significant at a significance of 1%?
 _________ Can we support the hypothesis that family size is decreasing in the FSM or not?
 _________ What is the pvalue for this hypothesis test?
 _________ What is the largest possible confidence interval for which this difference is significant?
Statistic or Parameter 
Symbol 
Equations 
Excel 
Hypothesis Testing 
Degrees of freedom 
df 
= n1 
=COUNT(data)1 
Calculate a tstatistic (t) 
t 

(x  µ)/(sx/sqrt(n)) 
Calculate tcritical for a twotailed test 
t_{c} 

=TINV(α,df) 
Calculate a pvalue from a tstatistic t 
p 

= TDIST(ABS(t),df,#tails) 