The Gestation data set contains birth weight, date, and gestational period collected as part of the Child Health and Development Studies. Information about the baby’s parents-age, education, height, weight, and whether the mother smoked is also recorded.

1. (Sampling distribution)

Calculate and interpret a 95% confidence interval for the mean age of mothers from the classic Gestataion data set from the mosaicData package.

(A 95% confidence interval for a mean is constructed by taking the estimate and adding and subtracting two standard deviations.)

2. (Bootstrap sampling distribution)

Use the bootstrap to generate and interpret a 95% confidence interval for the median age of mothers for the classic Gestation data set from the mosaicData package.

3. (Confidence interval)

We saw that a 95% confidence interval for a mean was constructed by taking the estimate and adding and subtracting two standard deviations. How many standard deviations should be used if a 99% confidence interval is desired?

4. (Missing value)

A data scientist working for a company that sells mortgages for new home purchases might be interested in determining what factors might be predictive of defaulting on the loan. Some of the mortgagees have missing income in their data set. Would it be reasonable for the analyst to drop these loans from their analytic data set? Explain.

5. (Simple linear regression)

Fit a linear regression model for birthweight (wt) as a function of the mother’s age (age).

Use a graphical means to convey your finding.

6. (Bootstrap sampling distribution)

Use the bootstrap to generate a 95% confidence interval for the regression parameters in a model for weight as a function of age for the classic Gestation data set from the mosaicData package.