Questions: Construct a 95% confidence interval estimate for the difference between two population means based on the following information: Population 1 Population 2 barx1=355 barx2=320 sigma1=50 sigma2=40 n1=50 n2=80

Solution Steps

To construct a 95% confidence interval estimate for the difference between two population means, we can use the following steps:

1. Calculate the point estimate of the difference between the two means.
2. Determine the standard error of the difference between the two means.
3. Find the critical value for a 95% confidence level.
4. Construct the confidence interval using the point estimate, the critical value, and the standard error.

The point estimate of the difference between the two population means is given by: \[ \bar{x}_1 - \bar{x}_2 = 355 - 320 = 35 \]

The standard error of the difference between the two means is calculated as: \[ \text{SE} = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} = \sqrt{\frac{50^2}{50} + \frac{40^2}{80}} = \sqrt{50 + 20} = \sqrt{70} \approx 8.3666 \]

For a 95% confidence level, the critical value \( z_{\alpha/2} \) is: \[ z_{\alpha/2} \approx 1.960 \]

The margin of error (ME) is calculated as: \[ \text{ME} = z_{\alpha/2} \times \text{SE} = 1.960 \times 8.3666 \approx 16.3982 \]

The confidence interval is then: \[ (\bar{x}_1 - \bar{x}_2) \pm \text{ME} = 35 \pm 16.3982 \]

Final Answer