Question

A random sample of size n = 21, taken from a normal population with a standard deviation 04 =5, has a mean X4 = 90. A second random sample of size n2 = 37, taken from a different normal population with a standard deviation o2 = 4, has a mean X2 = 39. Find a 94% confidence interval for 11 - H2 Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The confidence interval is <H2-H2= (Round to one decimal place as needed.)

Answer 1

To calculate the confidence intervel we will use z distribution because standard deviation is known.

= 3.9 Given that For Ist population, n = 21 = 5 u = 90 for sercond kodulation ng= 37, T2 = 4,8g The 99% confidence interval for the difference of means M-te is given by (57-1g) + 9.58 үч ng = (40-39 I 2.58 52 + 4 91 37 51 + 9.58 x 1.2739 51 t. 3.28 67 SI- 3.9867, S1+3.9867 = (47.7133, 54-2867) 47.7133 L M - Mg L 54.2867 ( Exact value) 47.7 L Mita L 54.3 (Rounded Vahre) Sol