Question

An ecologist randomly samples 19 plants of a specific species and measures their heights. He finds that this sample has a mean of 15 cm and a standard deviation of 4 cm. If we assume that the height measurements are normally distributed, find a 90% confidence interval for the mean height of all plants of this species. Then complete the table below.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

What is the lower limit of the confidence interval? What is the upper limit of the confidence interval?

Answer 1

Solution :

Given that,

n = 19

= 15   

s = 4

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

Our aim is to construct 90% confidence interval.   

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05

Also, d.f = n - 1 = 18  

    =    =  0.05,18 = 1.734

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

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.734* ( 4/ 19 )

= 1.591

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

( - E ) <   <  ( + E)

( 15 - 1.591 )   <   <  ( 15 + 1.591)

13.4 <   < 16.6

Required 90% confidence interval is ( 13.4 , 16.6 )

The lower limit of the confidence interval = 13.4

The upper limit of the confidence interval = 16.6