Question

We wish to estimate μ , the mean mass (in kg) of the Sandhill Crane. We take a random sample of 20 Sandhill Cranes and measure their masses. For this sample, we find an average mass of 4.53 kg and a standard deviation of 0.8 kg. Assuming the masses are normally distributed. Find the upper limits of 98% confidence interval for μ . Select the closest to your answer. options: 4.70 5.20 4.90 4.80 5.10 5.00

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 4.53

sample standard deviation = s = 0.8

sample size = n = 20

Degrees of freedom = df = n - 1 = 20 -1 = 19

At 98% confidence level

= 1-0.98% =1-0.98 =0.02

/2 =0.02/ 2= 0.01

t/2,df = t0.01,19

t/2,df = 2.539

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

= 2.539 * (0.8 / 20)

Margin of error = E = 0.454

The 98% confidence interval estimate of the population mean is,

- E < <  + E

4.53 - 0.454 < <4.53 + 0.454

4.08 < < 4.98

(4.08,4.98)

Upper limit = 4.98

Option- 5.00