# Single Sample Inferences

Math_

In Inferential Statistics we saw that the methods of data interpretation depend, among other things, on the number of samples involved …. are different depending on the size, n, of the sample(s) under consideration. Here we examine situations where the sample size is large; that is, where n > 30.

Suppose, for example, that ACME Electronics wishes to perform a quality control on a sample of a new line of LCD projectors. Equipped with a ‘TI-83 plus’ graphics calculator a quality control engineer records the following projector lifetimes, measured in days, as:

L1 = {1395, 1295, 1415, 1335, 1435, 1265, 1455, 1375, 1475, 1485, 1495, 1505, 1515, 1525, 1530, 1535, 1540, 1545, 1550, 1552, 1555, 1557, 1560, 1565, 1565, 1565, 1570, 1573, 1575, 1578, 1580, 1585, 1590, 1595, 1600, 1605, 1615, 1625, 1635, 1645, 1655, 1835, 1675, 1795, 1695, 1865, 1715, 1755, 1735},

where L1 is a ‘TI-83 plus’ data list.

1-var stats –> n = 49, so the sample is large

further, xbar = 1565 days, s = 121.7 days

H0: mu = 1600 days vs Ha: mu not= 1600 days

two-tailed z-Test –> z = -2.01

when alpha = .05, zc = 1.96 because invNorm(.975) = 1.9599… ~ 1.96.

when alpha = .01, zc = 2.58 because invNorm(.995) = 2.5758… ~ 2.58.