A 95% confidence interval (using the conservative value for the degrees of freedom) for
A 95% confidence interval (using the conservative value for the degrees of freedom) for
μ1 − μ2, based on two independent samples of sizes 18 and 20, respectively, gives us (45.6,
56.7).
(a) What was the observed difference between the two sample means x¯1 and x¯2?
(b) What would be the margin of error for a 99% confidence interval for μ1 − μ2?
(c) Answer each of the following questions with yes, no, or can’t tell.
i. Is the difference between the two population means, μ1 − μ2, included in the 95%
confidence interval?
ii. Is the difference between the two sample means, x¯1 − x¯2, included in the 95%
confidence interval?
iii. Is the probability that the difference between the two population means, μ1 − μ2,
falls between 45.6 and 56.7 equal to 0.95?
iv. If larger samples were used to calculate the confidence interval, would it include
more values for the difference between the two population me
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