A researcher wants to estimate the difference in the means of two populations.A random sample of 36 items from the first population results in a sample mean of 430.A random sample of 49 items from the second population results in a sample mean of 460.The population standard deviations are 120 for the first population and 140 for the second population.From this information, a 95% confidence interval for the difference in population means is _______.
A)-95.90 to 35.90
B)-85.44, 25.44
C)-76.53 to 16.53
D)-102.83 to 42.43
E)98.45 to 125.48

Question

Quizplus · Accepted Answer

The confidence interval for the difference in means is calculated using the formula for the confidence interval of the difference between two means with known population standard deviations. The interval is calculated as (mean1 - mean2) ± Z * sqrt((σ1^2/n1) + (σ2^2/n2)), where Z is the Z-score for 95% confidence (approximately 1.96). Plugging in the values, the interval is approximately -85.44 to 25.44.

A Researcher Wants to Estimate the Difference in the Means