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.

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 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  

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.

answer: d. $20

step-by-step explanation:

just took the test

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.