Question

MY NOTES

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):

71

102

126

123

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

Solution:

x	x2
71	5041
102	10404
126	15876
123	15129
60	3600
64	4096
∑x=546	∑x2=54146

Mean ˉx=∑xn

=71+102+126+123+60+646

=5466

=91

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√54146-(546)265

=√54146-496865

=√44605

=√892

=29.8664

Degrees of freedom = df = n - 1 = 6 - 1 = 5

At 75% confidence level the t is ,

= 1 - 75% = 1 - 0.75 = 0.25

/ 2 = 0.25 / 2 = 0.125

t /2,df = t0.0.125,5 =1.301

Margin of error = E = t/2,df * (s /n)

= 1.301 * (29.87 / 6)

= 15.86

Margin of error = 15.86

The 75% confidence interval estimate of the population mean is,

- E < < + E

91 - 15.86 < < 91 + 15.86

75.14 < < 106.86

Lower limit =75.14

Upper limit =106.86