Each car in a sample of seven cars was tested for nitrogen-oxide emissions (in grams per mile), and the following results were obtained. 0.07, 0.11, 0.15, 0.13, 0.12, 0.07, 0.13 a. assuming that this sample is representative of cars in use, construct a 95% confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars.

The 95% confidence interval would be given by (0.0825;0.1395)  

Step-by-step explanation:

1) 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".

Data: 0.07, 0.11, 0.15, 0.13, 0.12, 0.07, 0.13

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

represent the sample mean for the sample  

population mean (variable of interest)

s=0.0308 represent the sample standard deviation

n=7 represent the sample size  

2) Confidence interval

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

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, 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(0.025,6)".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 (0.0825;0.1395)    

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d