Question

The archaeologist discovered only nine fossil skeletons of an unknown species of miniature horse. Reconstructions of the skeletons of these miniature horses show the following shoulder heights ;

45.3 ​47.1 ​44.2 ​ 46.8 ​46.5 ​45.5 ​ 47.6 ​45.7 ​46.4

(a) Estimate the Sample Mean and Sample Standard Deviation.

(b) Using student’s t-distribution table, estimate the error E at 95% confidence.

(c) Estimate the interval of population mean having 95% confidence level.

Answer 1

Solution :

a) The sample mean is given as follows :

Where, xi's are sample values and n is sample size.

We have, n = 9

The sample mean is 46.122.

The sample standard deviation is given as follows :

We have, n = 9, and x̅ = 46.122

The sample standard deviation is 1.0462.

b) The error E at 95% confidence level is given as follows :

Where, t(0.05/2, ​​​​​​n - 1) is critical t value at 95% confidence level and (n - 1) degrees of freedom.

We have, s = 1.0462, n = 9

Using t-table we get,

Hence, error E at 95% confidence level is,

The error at 95% confidence level is 0.804.

c) The 95% confidence interval estimate of population mean is given as follows :

Where, x̅ is sample mean and E is error at 95% confidence level.

From part (a) and (b) we have,

x̅ = 46.122 and E = 0.804

Hence, 95% confidence interval estimate for population mean is,

The 95% confidence interval estimate for the population mean is (45.318, 46.926).

Please rate the answer. Thank you.