## In a climate survey, it was determined that in a random sample of 15 days, the average temperature in Kalamazoo at 2:00 PM in the months of

In a climate survey, it was determined that in a random sample of 15 days, the average temperature in Kalamazoo at 2:00 PM in the months of July and August is 73.38 degrees with a standard deviation of 3.798 degrees. Using this information, a 95% confidence interval for the average is (71.28, 75.48). Which of the following is the appropriate interpretation of this interval?

1)

We are certain that 95% of the days in the months of August and July will have a temperature at 2:00 PM between 71.28 and 75.48.

2)

We cannot determine the proper interpretation of this interval.

3)

We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM for the days recorded is between 71.28 and 75.48.

4)

We are 95% confident that the proportion of all days’ temperatures will fall between 71.28 and 75.48.

5)

We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM is between 71.28 and 75.48.

## Answers ( )

Answer:So on this case the 95% confidence interval would be given by (71.65;75.11)

The interval given for this case by the problem is:

(71.28, 75.48)

And the best conclusion is given by:

4) We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM is between 71.28 and 75.48.

Step-by-step explanation:Previous conceptsA

confidence intervalis “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 erroris 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

population mean (variable of interest)

represent the sample standard deviation

n=15 represent the sample size

95% confidence interval

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

(1)

The degrees of freedom are given:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a tabele to find the critical value. The excel command would be: “=-T.INV(0.05,14)”.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 (71.65;75.11)

The interval given for this case by the problem is:

(71.28, 75.48)

And the best conclusion is given by:

4) We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM is between 71.28 and 75.48.