An article presents a study of the effect of the subbase thickness on the amount of surface deflection caused by aircraft landing on an airport runway. In six applications of a 160 kN load on a runway with a subbase thickness of 864 mm, the average surface deflection was 2.28 mm with a standard deviation of 0.090 mm. Find a 90% confidence interval for the mean deflection caused by a 160 kN load. Round the answers to three decimal places.

So on this case the 90% confidence interval would be given by (2.206, 2.354)    

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".

represent the sample mean for the sample  

population mean (variable of interest)

s=0.090 represent the sample standard deviation

n=6 represent the sample size  

Solution to the problem

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 0.90 or 90%, 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(0.05,5)".And we see that

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

So on this case the 90% confidence interval would be given by (2.206, 2.354)    

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed