Question

23 Find the critical value SELECT ALL APPLICABLE CHOICES A) 4.075 B) 3.075 C) 31.319 D) 31.653 corresponding to a sample size of 15 and a confidence level of 99.0 percent 24 The confidence Interval for the standard SELECT ALL APPLICABLE CHOICES deviation is given by A) True B) False (n- 1)s2 25 The confidence Interval for variance is given SELECT ALL APPLICABLE CHOICES A) False B) True 26 SELECT ALL APPLICABLE CHOICES A) z - distribution B) t - distribution ơis UNKNOWN n 30 then we use 27

Answer 1

23) 99% confidence interval indicates that the significance level of $\alpha=1-99/100=0.01$ .

This is the total area under both right and left tails of $\chi^2$ distribution.

The are under the right tail is 0.01/2=0.005

The degrees of freedom is n-1=15-1=14, for a sample of size n=15

We go to the chi-square table and get a chi-square value of 31.3193 for df=14 for area under the right tail 0.005

This is the right tail critical value $\chi^2_R$

ans: C) 31.319

24) the confidence interval for variance $\sigma^2$ is

$\frac{(n-1)s^2}{\chi^2_R}<\sigma^2<\frac{(n-1)s^2}{\chi^2_L}$

and for the standard deviation is

$\sqrt\frac{(n-1)s^2}{\chi^2_R}<\sigma<\sqrt\frac{(n-1)s^2}{\chi^2_L}$

Hence the confidence interval given is not for standard deviation.

ans:B) False

25) The confidence interval for variance is

$\frac{(n-1)s^2}{\chi^2_R}<\sigma^2<\frac{(n-1)s^2}{\chi^2_L}$

The confidence interval given $\bar{x}-E<\mu<\bar{x}&plus;E$ is for mean

ans: A) False

26) We use the z distribution if $\sigma$ is known or n>30.

Since we have n>30, one of the above conditions is met. Hence we can use z-distribution.

ans: A) z-distribution.