According to the almanac, the mean age for a woman giving birth for the first time is 25.2 years. A random sample of ages of 35 professional women giving birth for the first time had a mean of 28.7 years and a standard deviation of 4.6 years. Use both a confidence interval and a hypothesis test at the 0.05 level of significance to test if the mean age of professional woman is different from 25.2 years at the time of their first birth.