Question

In a sample of 35 koalas, the sample mean weight was 9.41 kg, with a standard deviation of 1.38 kg.

a. What must be assumed before a t confidence interval to estimate the population mean?

b. Find and interpret a 99% confidence interval using the koala data. You will have to use your calculator’s “TInterval” on the “stats” setting because JMP requires the individual weights, which are not available.

c. If a future study aims to estimate the mean koala weight with a standard error of no more than 0.15 kg, what sample size should be used?

Answer 1

solution

Solution :

Given that,

sample mean = = 9.41

sample standard deviation = s = 1.38

sample size = n = 35

Degrees of freedom = df = n - 1 = 35 - 1= 34

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df =  t0.005,34 = 2.728

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

= 2.728* ( 1.38/ 35)

Margin of error = E =0.6363

The 99% confidence interval estimate of the population mean is,

- E < < + E

9.41 - 0.6363 < < 9.41 + 0.6363

8.7737 < < 10.0463

(8.7737 ,  10.0463)

The 99% confidence interval estimate of the population mean is fall between lower bound and upper bound (8.7737 ,  10.0463)