Tell whether each integer is prime, composite or neither

1. 5
2.8
3.13
4.18
5.73
6.36

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.