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. 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.

2. given a margin of error of 5.4 mm, construct a 95% confidence interval for the population mean height. enter only the lower limit for your confidence interval rounded to one decimal place.

3.given a margin of error of 5.4 mm, construct a 95% confidence interval for the population mean height. enter only the upper limit for your confidence interval rounded to one decimal place.

4. why is a point estimate alone usually insufficient for statistical inference?

a. a point estimate alone is insufficient because the sampling distribution is not centered at the parameter.
b. an interval estimate gives us a sense of the accuracy of the point estimate whereas a point estimate alone does not.
c. the point estimate usually falls outside the confidence interval.
d. the point estimate has a large standard deviation compared to other estimators.

1) The mean calculated for this case is

2)  

3)

4) B. An interval estimate gives us a sense of the accuracy of the point estimate whereas a point estimate alone does not.

Because with the confidence interval we know the confidence level of the interval, and the limits for the parameter at some significance level.  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part 1

In order to calculate the mean and the sample deviation we can use the following formulas:  

(a)  

(b)  

The mean calculated for this case is

The sample deviation calculated

population mean (variable of interest)

n=6 represent the sample size  

Part 2

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

  (1)

So if we have the margin of error 5.4mm we can find the lowr limit like this:

Part 3

Part 4

B. An interval estimate gives us a sense of the accuracy of the point estimate whereas a point estimate alone does not.

Because with the confidence interval we know the confidence level of the interval, and the limits for the parameter at some significance level.

the number of the people going.

step-by-step explanation:

the cost to buy one movie ticket is $7. if the total cost for the movie is a function of how many people go, then the input is : the number of the people going.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240