2. As a preliminary study to improve pregnancy outcomes of women in Tennessee, n=70 women were selected at random around Nashville and their gestational ages (time to birth in days) recorded. Assume that the average gestation age of women in the United States is 40 weeks, or 280 days (source, National Library of Medicine). Answer the following questions based on the output below. One-sample t test Variable Obs Mean Std. err. Std. dev. [95% conf. interval] gestat~e 76 260.3143 1.823648 15.25773 256.6762 263.9524 mean = mean(gestationtime) t = -10.7947 H0: mean = 280 Degrees of freedom = 69 Ha: mean 280 PrlT |t|) = 0.6006 PrlT > t) = 1.6066 a. Is there evidence that the mean gestational age in Nashville differs from the national average in the United States. Test the appropriate hypotheses at the 0.05 signicance level. Provide the test statistic, the degrees of freedom, the p-value, and the conclusion of the test. b. Present a 95% condence interval for the mean gestational age of women in Nashville, based on these data. c. What is the standard error of the sample mean for the of the gestational ages? d. What is the size of a typical deviation of a gestational age from the average gestational age