Question 1 10 pts The low.but 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: Use code to calculate the sample mean birth weight (birthwt) and sample standard deviation from this data then use them to find the value of the t-test statistic to determine if the average birth weight of all low-weight babies at the time of birth is more than 1075 grams. Question 2: Use pt() to find the probability of our sample statistic or more extreme, according to the test mentioned above in question 1. Make a conclusion about the result of the test at the 1% significance level. Question 3: Use qt() to find the cutoff t* value for a lower bound 99% confidence interval for the mean birth weight then calculate the confidence interval. Make a statement about the confidence interval and how this confirms your conclusion in question 3. Upload Choose a File