Question

Consider the following data for two independent random samples taken from two normal populations.

Sample 1	10	7	13	7	9	8
Sample 2	8	7	8	4	6	9

(a)Compute the two sample means.

Sample 1:

Sample 2:

(b)Compute the two sample standard deviations. (Round your answers to two decimal places.)

Sample 1:

Sample 2:

(c) What is the point estimate of the difference between the two population means? (Use Sample 1 − Sample 2.)

(d) What is the 90% confidence interval estimate of the difference between the two population means? (Use Sample 1 − Sample 2. Round your answers to two decimal places.)

_______to________

Answer 1

solution:-

(a) the two sample means

sample 1: 9

sample 2: 7

(b) the two sample standard deviations

sample 1: s1 = 2.28

sample 2: s2 = 1.79

(c) point estimate

=> (sample 1 - sample 2) = 9-7 = 2

(d) confidence interval

degree of freedom df = (n1+n2)-2 = (6+6)-2 = 10

we look into t table with df and with 90% confidence

critical value t = 1.812

confidence interval formula

=> point estimate +/- t * sqrt(s1^2/n1 + s2^2/n2)

=> 2 +/- 1.812 * sqrt((2.28^2/6) + (1.79^2/6))

=> -0.14 to 4.14