Question

How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds): 70 110 134 129 60 64 Assume that the population of x values has an approximately normal distribution. (a) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s. (Round your answers to one decimal place.) x = lb s = lb (b) Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.) lower limit lb upper limit lb

Answer 1

a)

Sample mean = X / n

= 567 / 6

= 94.5 lb

Sample standard deviation S = Sqrt [ X² - n ² / n-1 ]

= sqrt [ 59293 - 6 * 94.5² / 5 ]

= 33.8 lb

b)

t critical value at 0.25 significance level with 5 df = 1.301

75% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

94.5 - 1.301 * 33.8 / sqrt(6) < < 94.5 + 1.301 * 33.8 / sqrt(6)

76.5 < < 112.5

Lower limit = 76.5 lb

Upper limit = 112.5 lb