Question

8. Suppose the mean of rim diameter of 31 ceramic vessels is 15.8 cm with standard deviation is 3.3 em. The diameter ofceramic vessels is normally distributed. Compute a 90% confidence interval for the population mean μ ofrim diameters for such ceramic vessels found at the archaeological site. (6 points) 65 the mean of rim dicemete, s 15,8 .69( s between 476cm an 16,937 s-H.740
need help to correct my mistake

Answer 1

Solution

given: sample size (n) 31, sample mean (15.8, sample standard deviation (s)- 3,5

Since population standard deviation (σ) is unknown, use t-distribution

degrees of freedom-n-1 31-1-30

for 90% confidence level with degrees of freedom = 30

t.697 (fromt - table)

formula : confidence interval for the population mean, μ

$=\bar x \pm t_{\frac{\alpha }{2}}*\left \{ \frac{s}{\sqrt{n}} \right \}$

3.5 = 15.8 ± 1.697 * 〈 〉

15.8 ± 1.07

Lower Limit-15.8-1.07 14. T3

Upper Limit = 15.8 + 1.07 16.87

We are 90% confident that the population mean of rim diameters for such ceramic vessels found at the archaeological site is from 14.73 cm to 16.87 cm.