Concept explainers
CI and two-sided tests correspond Refer to the previous two exercises. Using significance level 0.05, what decision would you make? Explain how that decision is in agreement with whether 0 falls in the confidence interval. Do this for the data for both the boys and the girls.
12.16 More boys are bad? 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 = life length (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?
12.17 More boys are bad? 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 = life length (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?
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