The low.bwt data frame contains information for a random sample of 100 low birth weight infants born in two teaching hospitals in Boston, Massachusetts.

The dataset contains the following variables:

- birthwt: the weight of the infant at birth, measured in grams - gestage: the gestational age of the infant at birth, measured in weeks - momage: the mother's age at the birth of the child, measured in years - toxemia: recorded as Yes if the mother was diagnosed with toxemia during pregnancy, and No otherwise - length: length of the infant at birth, measured in centimeters - headcirc: head circumference of the infant at birth, measured in centimeters

Question 1:

The condition toxemia, also known as preeclampsia, is characterized by high blood pressure and protein in urine by the 20th week of pregnancy; left untreated, toxemia can be life-threatening.

Use the table() function with the variable toxemia to find the proportion of mothers in this sample that were diagnosed with toxemia. Then find and interpret a 96% confidence interval for the proportion of low-birthweight babies in which the mother was diagnosed with toxemia.

Question 2:

The average length of all low-weight babies at the time of birth has been known to be 36.5 centimeters with a standard deviation of 2.4 cm. We want to perform a hypothesis test to determine if the mean weight has changed. To perform this test, use code to find the mean length for our sample, calculate the value of the z-test statistic, and calculate the p-value for our sample data. State the conclusion of the test in context based on your results.