## Ecologists wanted to estimate the mean biomass (amount of vegetation) of a certain forested region. The ecologists divided the region into p

Ecologists wanted to estimate the mean biomass (amount of vegetation) of a certain forested region. The ecologists divided the region into plots measuring 1 square meter each, and they selected a random sample of 9 plots. The mean biomass of the 9 plots was 4.3 kilograms per square meter (kg/m2) and the standard deviation was 1.5 kg/m2 . Assuming all conditions for inference are met, which of the following is a 95 percent confidence interval for the population mean biomass, in kg/m2?

A) 4.3±1.96 (underroot 1.5/3).

B) 4.3±1.96 (1.5/3).

C) 4.3 ± 2.306 (underroot 1.5/9).

D) 4.3±2.3064 (1.5/9).

E) 4.3+2.30/15 (1.5/3).

## Answers ( )

Answer:, option c

Step-by-step explanation:We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The

first stepto solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. Sodf = 9 – 1 = 8

95% confidence intervalNow, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.306

The margin of error is:In which s is the standard deviation of the sample and n is the size of the sample.

Confidence interval:The confidence interval is the sample mean plus/minus the margin of error. So

The correct answer is given by

option c.