Question

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.
Two types of flares are tested and their burning times are recorded. The summary statistics are
given below.
Brand X
n=35
x-19.4 min
s=1.4 min
Brand Y
n=40
x=15.1 min
s-0.8 min
Construct a 95% confidence interval for the differences between the mean burning time of the
brand X flare and the mean burning time of the brand Y flare.
OPTIONS:
A) 3.2 min C) 3.5 min B) 3.8 min D) 3.6 min

Answer 1

Answer: D

Explanation:

To construct a 95% confidence interval for the difference between the means, we use the formula:

CI = x1 - x2 ± t*SE where x1 and x2 are the sample means, SE is the standard error of the difference, and t is the critical value from the t-distribution for a given confidence level and degrees of freedom.

SE = sqrt(s1^2/n1 + s2^2/n2) where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

The degrees of freedom can be calculated as:

df = n1-1 + n2-1 = 34 + 39 = 73

Using a t-distribution table with a confidence level of 95% and df=73, the critical value t is 1.996.

Plugging in the values, we have:

CI = 19.4 - 15.1 ± 1.996 * sqrt(1.4^2/35 + 0.8^2/40)

CI = 4.3 ± 1.996 * 0.38

CI = 4.3 ± 0.77

CI = (3.53, 5.07)

Therefore, the 95% confidence interval for the difference between the mean burning time of brand X and brand Y is (3.53, 5.07) minutes. So, the answer is D) 3.6 min.

Hope this helps, correct me if I’m wrong.