1) Examine the data set age-at-menarche which describes the age when a female experiences her first menstrual cycle. The study compared women who were born in 1990-1994 with women who were 80-84 when these data were collected). This problem uses the age-at-menarche dataset.

a) Researchers wanted to test whether age-at-menarche was getting younger over time.One paragraph in the reading is taken verbatim here:

White girls in the United States now menstruate at an average age of 12.6 years and black girls at 12.1 years, while Mexican American girls menstruate at an average age of 12.2 years (though it is not clear how far these differences in menarche can be traced back, since most of the historical documentation focuses on white American and European girls).

All the women in the data set were white. Test whether our data on younger women could have come from a population of young black women. Be sure to state the null hypothesis, whether you reject it, and at what p-value. Give a careful definition of the p-value. Also interpret the 95%CI. (1=younger, 0=older)

-> group = 1

One-sample t test

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Variable | Obs Mean Std. err. Std. dev. [95% conf. interval]

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aam | 15 12.48 .2125133 .8230606 12.0242 12.9358

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mean = mean(aam) t = 1.7881

H0: mean = 12.1 Degrees of freedom = 14

Ha: mean 12.1

Pr(T |t|) = 0.0954 Pr(T > t) = 0.0477

b) Test whether our sample of older white women is consistent in age-at-menarche with a sample of younger Mexican-American women. Be sure to state the null hypothesis, whether you reject it, and at what p-value. Give a careful definition of the p-value. Also interpret the 95%CI.

X=older Y= younger

Two-sample t test with equal variances Obs Mean Sto. err. Std. dev. [95% conf. interval] X 15 13. 59 . 2933333 1. 136875 12. 96086 14. 21914 15 12 . 48 . 2125133 . 8230606 12. 0242 12. 9358 Combined 30 13. 035 . 2056583 1. 126393 12. 6144 13. 4556 diff 1. 11 . 3622242 . 3680174 1. 851983 diff = mean (x) - mean(y) t 3. 0644 Ha: diff = e Degrees of freedom = 28 Ha: diff a Pr(T |t|] = 0.0848 Pr(T > t) = 0. 8024