A botanist measures the heights of 16 seedlings and obtains a mean and standard deviation of 72.5 cm and 4.5 cm,respectively.Find the 95% confidence interval for the mean height of seedlings in the population form which the sample was selected.
A)[62.91 82.09]
B)[70.30 74.70]
C)[70.10 74.90]
D)[70.54 74.46]
E)[71.90 73.10]

Question

Quizplus · Accepted Answer

We will use the formula: 
CI= x̄ ± z(α/2) * (σ/√n)
where:
x̄ = sample mean = 72.5
σ = standard deviation = 4.5
n = sample size = 16
α = level of significance = 0.05 (for 95% confidence interval, α = 1-0.95 = 0.05)
z(α/2) = z-score corresponding to α/2=0.025 from the standard normal distribution table.
z(0.025) = 1.96 
Putting the values in the formula, we get
CI = 72.5 ± 1.96 * (4.5/√16)
CI = 72.5 ± 1.96 * 1.125
CI = 72.5 ± 2.204
CI = [70.296, 74.704]
Therefore, the best choice is C: [70.10 74.90], as it is closest to the calculated confidence interval.

A Botanist Measures the Heights of 16 Seedlings and Obtains