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 as follows: 53.1, 60.2, 60.6, 62.1, 64.4, 68.6. Given a margin of error of 5.4 mm, construct a 95% confidence interval for the population mean height.

Answer 1

Answer: The required confidence interval is (56.1,66.9).

Explanation:

Since we have given that

53.1, 60.2, 60.6, 62.1, 64.4, 68.6

`\bar{x}=(53.1+60.2+60.6+62.1+64.4+68.6)/(6)=(369)/(6)=61.5`

n = 6

Margin of error = 5.4

At 95% level of confidence, z = 1.96

So, the confidence interval would be

`\bar{x}\pm \text{Margin of error}\\\\=61.5\pm 5.4\\\\=(61.5-5.4,61.5+5.4)\\\\=(56.1,66.9)`

Hence, the required confidence interval is (56.1,66.9).