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 had the following weights (pounds): 68 108 132 127   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.

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.)

Answer 1

Solution :

We are given a data of sample size n = 6

68,108,132,127,60,64

Using this, first we find sample mean() and sample standard deviation(s).

=   

= (68 + 108.......+ 64)/6

= 93.17

Now ,

s=   

Using given data, find Xi - for each term.Take square for each.Then we can easily find s.

s = 33.03

Note that, Population standard deviation() is unknown..So we use t distribution.

Our aim is to construct 75% confidence interval.

   c = 0.75

= 1 - c = 1 - 0.75 = 0.25

  /2 = 0.25 2 = 0.125

Also, d.f = n - 1 = 5  

    =    =  0.125,5 = 1.301

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n )

= 1.301* (33.03 / 6 )

= 17.543

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

( 93.17 - 17.543 )   <   <  ( 93.17+ 17.543)

75.6 <   < 110.7

Required 99% confidence interval is ( 75.6 , 110.7 )