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.
1. Given a margin of error of 5.4 mm, construct a 95% confidence interval for the population mean height.
2. What is the point estimate of the population mean height of this variety of seedling 14 days after germination? Do not round your final answer.

1)

And the margin of error for this case is

And the confidence interval would be:

2) For this case the best estimator for the population mean is given by the sample mean:

And the reason of this is beacuse is an unbiased estimator of the parameter:

Step-by-step explanation:

Data given:

53.1, 60.2, 60.6, 62.1, 64.4, 68.6.

We can calculate the sample mean with the following formula:

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Part 1

The confidence interval for the mean is given by the following formula:

  (1)

Or equivalently:

And the margin of error for this case is

And the confidence interval would be:

Part 2

For this case the best estimator for the population mean is given by the sample mean:

And the reason of this is beacuse is an unbiased estimator of the parameter:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

answer: input the dimensions of the room to be painted. click the button to calculate the amount of paint and man-hours needed for this job.

interior paint coverage depends on the brand of paint used. the coverage amount is listed on the label of the paint can. use this to adjust the values in the paint coverage section below. paint usually is applied at 350 to 400 square feet per gallon (primer at 200 to 300 square feet per gallon).

step-by-step explanation: