MATH SOLVE

3 months ago

Q:
# Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Independent samples from two different populations yield the following data. x1 = 958, x2 = 157, s1 = 77, s2 = 88. The sample size is 478 for both samples. Find the 85% confidence interval for μ1 - μ2. 781 < μ1 - μ2 < 821 800 < μ1 - μ2 < 802 794 < μ1 - μ2 < 808 793.2946 < μ1 - μ2 < 808.7054

Accepted Solution

A:

Answer:Step-by-step explanation:The formula for determining the confidence interval for the difference of two population means is expressed as Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)Where x1 = sample mean of type A paintx2 = sample mean of type B paints1 = sample standard deviation type A paints2 = sample standard for type B paintn1 = number of samples of type A paintn2 = number of samples of type B paintFrom the information given,x1 = 75.7s1 = 4.5n1 = 11x2 = 64.3s2 = 5.1n2 = 9x1 - x2 = 75.7 - 64.3 = 11.4√(s1²/n1 + s2²/n2) = √(4.5²/11 + 5.1²/9) = √4.709Degree of freedom = (n1 - 1) + (n2 - 1)df = (11 - 1) + (9 - 1) = 18For the 98% confidence interval, the z score from the t distribution table is 2.552Margin of error = 2.552√4.709 = 5.55The upper boundary for the confidence interval is 11.4 + 5.55 = 16.95 hoursThe lower boundary for the confidence interval is 11.4 - 5.55 = 5.85 hoursThe correct option is B. 5.85 hrs < μ1 - μ2 < 16.95 hrs