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STA462/562 R HW- 2 (20pts) Name___________________

In this homework, you will apply knowledge from Chapters 7 & 8 in the analysis of the real data. A failure to submit both RMD and HTML (or pdf) files on Canvas will automatically result is a 10-pounts penalty.
Q1. (5pts)
In the R-demo shown in class, we used the data on infant birthweight collected at Baystate Medical Center, Springfield, Mass during 1986. The data is stored in R library MASS
Library(MASS)
data(birthwt)
a)Develop a confidence interval for a proportion of babies born from smoking mothers.
b)Provide the formula for pivotal quantity used in computation of this interval. Provide a formula for the 95% CI of the true proportion.
c)Develop a confidence interval for a proportion of babies born from nonsmoking mothers.
d)Find the confidence interval for the difference between proportions of babies born for these two groups.
e)Define the pivotal quantity used in d).
Use R to answer all of the questions above.

Q2. (5pts)
Use the same data set as in Q1 to develop the estimators of the mean and median for baby’s weight (use only smoking mothers).
a)Develop a sampling distribution of the mean using bwt variable. Use a bootstrap.
b)Develop a sampling distribution of the median using bwt variable. Use a bootstrap.
c)Compute bias, MSE, and 95% CI for a)
d)Compute bias, MSE, and 95% CI for b)
e)Summarize your findings. Minimum 5 full sentences are required.
Use R to answer all of the questions above.

Q3. (5pts)
Use the same data set as in Q1 to develop an estimators of the 95% quantile of weights (bwt) . Use only nonsmoking mothers.
a)Develop a sampling distribution of this estimator. Use a bootstrap.
b)Compute bias, MSE, and 95% CI for a)
c)Summarize your findings
Use R to answer all of the questions above.

Q4. (5pts)
Write a paragraph (min 5 full sentences) reflection on how this homework helped you understand concepts presented in Chapter 7 and Chapter 8.

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