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): 74 109 132 124 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 = Correct: Your answer is correct. lb s = 251.7 Incorrect: Your answer is incorrect. 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

#	X	Mean	(x - mean)2
1	74	93.800	392.040
2	109	93.800	231.040
3	132	93.800	1459.240
4	124	93.800	912.040
5	60	93.800	1142.440
6	64	93.800	888.040
Total	563		5024.84

Mean = 563 / 6 = 93.8

Standard deviation = Sqrt(SS / n - 1) = Sqrt(5024.84 / 5) = 31.7

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(b) 75% Confidence interval for the weight of mountain lions:

From the data: , = 93.8, s = 31.7, n = 6

Since population standard deviation is unknown, the tcritical (2 tail) for = 0.25, for df = n -1 = 5, is 1.301

The Confidence Interval is given by ME, where

The Lower Limit = 93.8 - 16.8 = 77.0

The Upper Limit = 93.8 + 16.8 = 110.6

The 75% Confidence Interval is (77.0 , 110.6)

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