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 t-test 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 xd of -2.25 and a sample standard deviation of the difference sd 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.

  1. sample size: n = ______________
  2. sample mean xd = ______________
  3. sample standard deviation sd = ______________
  4. alpha: α = ______________
  5. degrees of freedom: = ______________
  6. t-critical: tc = ______________
  7. t-statistic: t = ______________
  8. At a 1% risk of rejecting a true null hypothesis:
    1. ___ Reject the null hypotheis? OR
    2. ___ Fail to reject the null hypothesis?

  9. _________ Is the difference in the number of siblings between the generations statistically significant at a significance of 1%?
  10. _________ Can we support the hypothesis that family size is decreasing in the FSM or not?
  11. _________ What is the p-value for this hypothesis test?
  12. _________ 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 = n-1 =COUNT(data)-1
Calculate a t-statistic (t) t xbartot (1K) (x - )/(sx/sqrt(n))
Calculate t-critical for a two-tailed test tc =TINV(α,df)
Calculate a p-value from a t-statistic t p = TDIST(ABS(t),df,#tails)