Answer to Question #314449 in Statistics and Probability for naruto

Question

A study by Thienprasiddhi et al. (A-4) examined a sample of 16 subjects with open-angle glaucoma

and unilateral hemifield defects. The ages (years) of the subjects were:

62 62 68 48 51 60 51 57

57 41 62 50 53 34 62 61

Can we conclude that the mean age of the population from which the sample may be presumed to have been drawn is less than 60 years? Let alpha = 0.5

Answer 1

$\mu =(62+62+68+48+51+60+51+57+57+41+62+50+53+34+62+61)/16=65.4$

$\sigma=\sqrt{\frac{11.56+11.56+6.76+302.76+207.36+29.16+207.36+70.56+70.56+595.36+11.56+237.16+153.76+985.96+11.56+19.36}{\sqrt{15}}}=27.5$

$\mu=65.4 \plusmn z_{\alpha/2} \frac{\sigma}{\sqrt{n}}=65.4 \plusmn 1.649 \frac{27.5}{\sqrt{16}}=65.4 \plusmn 11.3$

It can be as smaller 60 as no