3. (21 marks) 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 x = 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 5% 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 90% 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) 2 STAT 151 Assignment 4 Total: 1 19 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)