Question

If n < 30 and σ İs unknown, then the 100(1-α)% confidence interval for a population mean is_ 7. assuming the population is normally distributed xtra 21 1(degrees of freedom = n-2) a. 1 (degrees of freedom-n-1) c. t(degrees of freedom-n-1) 1 d. x ± te |--| (degrees of freedom n-2) 1 (degrees of freedom = n-1) If n interval when the level of confidence is 99% 8. 16, then find the number ta2 needed in the construction of a confidence a. 2.583 b. 2.602 c. 2.921 d. 2.947 e. 2.977

Answer 1

7. when n < 30 and $\sigma$ is unknown we perform a t-test.

100(1-$\alpha$)% confidence interval for the population mean:

$\textbf{Ans: b. }\bar x \pm t_{\alpha/2}\left [ \frac{s}{\sqrt{n}} \right ] (\textup{degree of freedom = n-1})$

8. n = 16

df = n-1 = 15

$\alpha = 100 - 99 = 1\% = 0.01$

Using excel function : = T.INV.2T(0.01,15)

$t_{\alpha/2} = \textbf{2.947}$

Answer d.