Refer to Exercise 6.3.6.
(a) Without doing any computations, would an 80% confidence interval for the data in Exercise 6.3.6 be wider, narrower, or about the same? Explain.
(b) Without doing any computations, if 500 mice were sampled rather than 86, would the 95% confidence interval listed in Exercise 6.3.6 be wider, narrower, or about the same? Explain.
Exercise 6.3.6
A zoologist measured tail length in 86 individuals, all in the 1-year age group, of the deermouse Peromyscus. The mean length was 60.43 mm and the standard deviation was 3.06 mm. A 95% confidence interval for the mean is (59.77,61.09).
(a) True or false (and say why): We are 95% confident that the average tail length of the 86 individuals in the sample is between 59.77 mm and 61.09 mm.
(b) True or false (and say why): We are 95% confident that the average tail length of all the individuals in the population is between 59.77 mm and 61.09 mm.