According to Canadian literature, the mean age at which toddlers first put 2 words together is 19 months, and the standard deviation is 0.33 months. A pediatrician wishes to study whether the mean age may differ from 19 months, by observing toddlers that visit her practice. The pediatrician works one Saturday a month, and one Saturday, she surveys the 6 toddlers who visit her practice by asking their parent(s) at what age their child put first 2 words together; the data are {19.2, 18.1, 17.3, 19.4, 18.4, 18.6} months, and the sample mean is = 18.5 months. The pediatrician assumes the population standard deviation is 0.33 months, as stated in Canadian literature. a) Construct and interpret a 95% two-sided confidence interval for the average age (in months) at which toddlers first put two words together. (6 marks) b) Does the interval in part (a) give evidence that the average age at which toddlers first put two words together differs from 19 months? Explain. (2 marks) c) Test at the 5% significance level whether the average age at which toddlers first put two words together differs from 19 months. (8 marks) d) For the above inferences to be valid, it is necessary for us to assume the sample is randomly selected from a normally distributed population. Are there any indications that either of these assumptions are violated? Explain. Hint: To check one of these assumptions, you will find it helpful to construct a histogram or a stem-and-leaf display. (4 marks)