Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2
n1 = 50 n2 = 35
X1 = 13.6 X2 = 11.6
1 = 2.2 1 = 3.0
1. What is the point estimate of the difference between the two population means?
2. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals).
3. Provide a 95% confidence interval for the difference between the two population means (to 2 decimals).

1. Point estimate Md = 2

2. The 90% confidence interval for the difference between means is (1.01, 2.99).

3. The 95% confidence interval for the difference between means is (0.82, 3.18).

Step-by-step explanation:

a) The point estimate of the difference between the two population means is the difference between sample means:  

2. We have to calculate a 90% confidence interval for the difference between means.

The sample 1, of size n1=50 has a mean of 13.6 and a standard deviation of 2.2.

The sample 2, of size n2=35 has a mean of 11.6 and a standard deviation of 3.

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

The degrees of freedom for this confidence interval are:

The critical t-value for a 90% confidence interval is t=1.663.

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

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

The 90% confidence interval for the difference between means is (1.01, 2.99).

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

The critical t-value for a 95% confidence interval and 83 degrees of freedom is t=1.989.

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 (0.82, 3.18).

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step-by-step explanation: