Estimation (Difference between 2 means) - Part 1

How many case or cases do you have for constructing a two-sided confidence for  $\mu_1-\mu_2$ ?

• 1

• 2

• 3

• 4

• 5

What statistical score will you use in the confidence interval for  $\mu_1-\mu_2$  when you know the values of  $\sigma_1^2$  and  $\sigma_2^2$  where  $\sigma_1^2=\sigma_2^2$  ?

•  $t_{\frac{\alpha}{2},\nu}$  

•  $\chi_{\frac{\alpha}{2},\nu}$  

•  $z_{\frac{\alpha}{2}}$  

A random sample A of size 25 gives a mean equal to 5 and another random sample B of size 32 gives a mean equal to 8. What is the point estimate for the difference between two unknown population means  $\mu_B-\mu_A$  ?

• 3

• 0.05

• -3

• -0.05

Suppose a 95% confidence interval for  $\mu_1-\mu_2$  is (0.5, 2), could there be any difference between $\mu_1$  and  $\mu_2$  with a 95% degree of confidence? 

• NO. 

• YES. 

• Not sure.

Suppose the information below is obtained from two random samples. Assume that  the population variances are equal, which statistical score will you use in constructing a 95% confidence interval for  $\mu_1-\mu_2$ ? $\overline{x}_1=20,\ \overline{x}_2=16,\ s_1=2,\ s_2=3,\ n_1=17,\ n_2=21.$ 

 


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•  $\chi_{0.025,36}^2$  

•  $t_{0.05,36}$  

•  $z_{0.025}$  

•  $t_{0.025,36}$