Here are the weights, in pounds, of a sample of 13 adult female golden retriever dogs: 59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4.a. what are the degrees of freedom, and what's the critical value of t needed to construct a 95% confidence interval for the population mean weight of adult golden retrievers? (4 points)b. can we use t procedures to do inference for the mean weight of the population of adult golden retrievers? explain, and include a sketch of a data plot. (6 points)c. construct a 95% confidence interval for the mean weight of the population of adult golden retrievers. show your work. (8 points)d. suppose someone was to do a test of the hypothesis h0 : m = 52. interpret the confidence interval you obtained in part c of this problem as it pertains to this hypothesis. (8 points)