Question

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 percent confidence interval for the mean height of seedlings in the population from which the sample was selected.

a. 170.54,7446)
b. 7010, 7490]
c. [70.30.7470
d. [62.91.82.09]
e. [71.90, 73101

Answer 1

c. [70.30, 74.70]

Explanation:

Confidence interval is a range of values in which there is a specified probability that the value of a parameter lies within that range.

The confidence interval of a statistical data can be written as.

x+/-zr/√n .......1

Given;

Mean gain x = 72.5 cm

Standard deviation r = 4.5 cm

Number of samples n = 16

Confidence interval = 95%

z (at 95% confidence) = 1.96 (from the table)

Substituting the values we have into equation 1;

72.5 +/- 1.96×4.5/√16

72.5 +/- 2.20 cm

[70.30, 74.70]

Therefore, the 95% confidence interval is

[70.30, 74.70] cm