Question

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow procedure that utilized water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those heights, measured in millimeters, were 54.8, 60.6, 60.2, 63.2, 65.6, 71.1 Using technology, construct a 99% confidence interval.

Answer 1

Sample observations : 54.8, 60.6, 60.2, 63.2, 65.6, 71.1

Total number of samples = n = 6.

Sample Mean = X̄ which is given as -

Sample Standard = s which is defined as-

Therefore, s = 5.52.

Confidence level = 99%

α = (1 - 0.99) / 2 = 0.005

degrees of freedom = df = n-1 = 5

t score = t = tα,n-1 = 4.03 (from table)

Confidence Interval for population mean (μ) is given as -

or,

or, 53.5 ≤ μ ≤ 71.66

There confidence interval is given as- (53.5,71.66)

Table from which we get t-value -