Question

A paleontologist examines 32 skeletons of a new species of dinosaur and finds that the average length of the right femur is 80 cm, with a standard deviation of 8 cm.

a. Does this involve z-values or t-values? Explain how you know this.

b. Estimate the population mean with 90% confidence.

Answer 1

a) t value is involve because population standard deviation is not known

b) The 90% confidence interval for population mean is

xbar - t_a/2 * ( s/n) < < xbar + t_a/2 * ( s/n)

for a = 0.10 and d.f = n -1 = 31

t_{0.05 , 31} = 1.70

80 - 1.70 * (8/32) < < 80 + 1.70 *( 8/32)

77.60 <   < 82.40