The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error = 0.5 inches
z = found by using a z-score table
SD = sample standard deviation = 1.3 inches
n = sample size
At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.647
Plug in the values to the formula and solve for the sample size, n.
MOE = z x (SD / √n)
0.5 = 1.647 x (1.3 / √n)
√n = 1.647(1.3) / 0.5
n = 18.34
n = 18
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