You select a random sample of n=14 families in your neighborhood and find the following family sizes (number of people in the family)

15, 16, 19, 18, 17, 15, 16, 16, 15, 16, 15, 16. 17, 18

a. what is the best estimate for the mean family size for the population of all families in a country?

(round to the nearest tenth as needed)

b. what is the 95% confidence interval for the estimate?

__
(round to the nearest tenth as needed)

c. comment on the reliability of the estimate. choose the correct answer below.

the sample is unlikely to be very representative of all families in a country.

the sample is unlikely to be representative of all families in a country.

there is not enough data to make a conclusion.

a)

represent the sample mean  

b) The 95% confidence interval would be given by (15.620;17.094)  

c) The concept of very representative not exists. A asmaple can be representative or not of a population. So then based on this the best option is:

The sample is unlikely to be representative of all families in a country.

The reason is because we have just a sample of 14 if we want to be more confidence about the true population mean we can increase the sample size in order to have a better estimation.

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".  

The data given : 15, 16, 19, 18, 17, 15, 16, 16, 15, 16, 15, 16. 17, 18

We can calculate the mean and the sample deviation with the following formulas:

represent the sample mean  

population mean (variable of interest)  

represent the sample standard deviation  

n=14 represent the sample size  

Part a

The best estimate for the mean is the average given by:

represent the sample mean  

Part b

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

(1)  

The degrees of freedom are given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,13)".And we see that  

Now we have everything in order to replace into formula (1):  

So on this case the 95% confidence interval would be given by (15.620;17.094)  

Part c

The concept of very representative not exists. A asmaple can be representative or not of a population. So then based on this the best option is:

The sample is unlikely to be representative of all families in a country.

The reason is because we have just a sample of 14 if we want to be more confidence about the true population mean we can increase the sample size in order to have a better estimation.

the best buy, is the 4- kilogram bag of lollipops for $18.40.

step-by-step explanation:

i found my answer by dividing the cost of each bag by their respective weights.

14.88 divided by 2 = 7.44

17.29 divided by 3 = 5.77

18.4 divided by 4 = 4.6

24.4 divided by 5 = 4.88

by this, i found that the 4 kilo bag is the best buy.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.