3. The average weight of new-born kittens is 3.5 ounces. A breeder suspects one of her cats, Stella, produces extra small kittens. The breeder's suspicions arise from the weights of Stella's most recent litter of kittens: {3.1, 3.3, 3.0, 3.7, 2.9, 2.9}. Note that the sample mean is 3.15 oz. Assume that the standard deviation of the weight of all Stella's new-born kittens is 0.3 oz. a) Test at the 1% significance level whether the average weight of Stella's new-born kittens is below 3.5 oz. Complete all 6 steps of your hypothesis test, including a discussion of the assumptions. (8 marks) b) Obtain and interpret a 95% two-sided confidence interval for the mean weight of all Stella's new-born kittens (6 marks)

c) Does the interval in part (b) give evidence that the average weight of Stella's new-born kittens differs from 3.5 oz? Explain. (3 marks)

d) In order 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).