Question

Confidence Interval about a Population Mean 2) Consider the same information as in Example 2 on page 320, section 7.2, but use the following summary values instead: the sample size to be n = 15, the sample mean i = 30.2, and the sample standard deviation s = 2.40. The given summary statistics resulted from the raw data: 31, 29, 31, 26, 31, 32, 35, 28, 30, 27, 29, 29, 30, 32, and 34. Write your solution just like in the example. Show all work and use the formulas (do not use technology here!) Note that the solution shown in the example is quite detailed. Your solution could be shorter, start where it says Using Distribution Table on page 321, and continue from there.

Answer 1

n = 15 The given data 31, 29, 31, 26, 31, 31, 35, 28, 30, 27, 29,29,30,32 and 34 Sample meom. t = 30.2, standard deviation 5 = 2.40 The Critical value is to 02 - 2.145 We now find the morrgin of error & as Shown here: S forces - to. 025 cm 2.40 = 2.1458 √15 - 1.329208 with = 30.2 and E= 1.329208, we Construit confidence interval as X-E se te 30.2 - 1.329208 < ML 30.2 + 1.329208 28. 87 L M L 31.53 Interpretation: are 954 Confident that the limits of 28.8t ong and 31.53 kg actually do Contain the value of the population If we were to collect many Samples f 15 melhor on girls and fina the meam Deight in each Sample, about gox of resulting confidence interna Should conterim the value of the meam Weight of all mewborn girls. We meem pe. random