A study of 375 women who lived in pre-industrial Finland (by S. Helle et al., Science , vol. 296, p. 1085, 2002) using Finnish church records from 1640 to 1870 found that there was roughly a linear relationship between y = lifelength (in years) and x = number of sons the woman had, with a slope estimate of -0.65 (se = 0.29).
a. Interpret the sign of the slope. Is the effect of having more boys good, or bad?
b. Show all steps of the test of the hypothesis that life length is independent of number of sons, for the two-sided alternative hypothesis. Interpret the P-value.
c. Construct a 95% confidence interval for the true slope. Interpret. Is it plausible that the effect is relatively weak, with true slope near 0?