The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. Sample 1 Sample 2
Sample Mean 45 42
Sample Variance 85 90
Sample Size 10 12
1. The 95% confidence interval for the difference between the two population means is:.
a. 0b. 2c. 3d. 15
2. The standard error of (x-bar1)-(x-bar2) isa. 3.0b. 4.0c. 8.372d. 19.48

1. The 95% confidence interval for the difference between means is (-5.34, 11.34).

2. The standard error of (x-bar1)-(x-bar2) is 4.

Step-by-step explanation:

We have to calculate a 95% confidence interval for the difference between means.

The sample 1, of size n1=10 has a mean of 45 and a standard deviation of √85=9.2195.

The sample 2, of size n2=12 has a mean of 42 and a standard deviation of √90=9.4868.

The difference between sample means is Md=3.

The estimated standard error of the difference between means is computed using the formula:

The critical t-value for a 95% confidence interval is t=2.086.

The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 95% confidence interval for the difference between means is (-5.34, 11.34).

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: