Question

Listed below are student evaluation ratings of​ courses, where a rating of 5 is for​ "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a 90​% confidence level. What does the confidence interval tell about the population of all college students in the​ state?

3.9

3.1

3.7

4.4

3.2

4.1

3.3

4.4

4.3​,

4.4

4.5

3.9

3.2​

4.2,

4.0

USING EXCEL

What is the confidence interval for the population mean

muμ​?

What is the confidence interval for the population mean

muμ​?

<

​(Round to two decimal places as​ needed.)

What does the confidence interval tell about the population of all college students in the​ state? Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice.

A.

The results tell nothing about the population of all college students in the​ state, since the sample is from only one university.

B.We are 90​%

confident that the interval from

to actually contains the true mean evaluation rating.

​(Round to one decimal place as​ needed.)

C.

We are confident that

90​%

of all students gave evaluation ratings between

and .

​(Round to one decimal place as​ needed.)

Answer 1

The Confidence Interval is 3.68 to 4.13 at 90% Confidence Level

Option A is correct: "The results tell nothing about the population of all college students in the​ state, since the sample is from only one university."

Since these course ratings were obtained from one university only, it cannot be extended to represent students from all universities in that state because a number of different factors will create a different experience for the students in other universities.

Explanation:

Using excel, the mean for the given data was found to be 3.91 and the

Confidence Level (at 90.0%) was found to be 0.23 (correct to 2 decimal places)

To calculate the confidence interval for the population mean, you simply need to work out the lower and upper bounds for the mean value. Just subtract the confidence level from the mean and add the confidence level to the mean

Lower Bound: 3.91 - 0.23 = 3.68

Upper Bound: 3.91 + 0.23 = 4.13

Hope that answers the question. Have a great day!

Answer 2

Given Information:

Confidence level = 90%

population size = 15

Required Information:

confidence interval for the population mean = ?

Answer:

confidence interval for the population mean = 3.74 < μ < 4.13

Explanation:

We can find the confidence interval in excel using

confidence interval = μ ± confidence

Where μ is the mean of population and confidence is given by

CONFIDENCE(alpha, standard deviation, population size)

Where alpha is

alpha = 100% - Confidence level

alpha = 100% - 90%

alpha = 10%

alpha = 0.10

So we need to find mean and standard deviation first,

The population mean can be found by using AVERAGE(values) function in excel

The function returns a mean of

μ = 3.93

The standard deviation of population can be found by using STDEV.P(values) function in excel

The function returns a standard deviation of

ο = 0.46

Now the confidence value can be found

CONFIDENCE(alpha, standard deviation, population size)

CONFIDENCE(0.10, 0.46, 15)

The function returns confidence value of

confidence = 0.20

Therefore, the confidence interval is

confidence interval = μ ± confidence

confidence interval = 3.93 ± 0.20

Upper limit = 3.93 + 0.20 = 4.13

Lower limit = 3.93 - 0.20 = 3.74

confidence interval = 3.74 < μ < 4.13

This confidence interval tell us that we are 90% confident that the student evaluation ratings of​ courses are from 3.74 to 4.13 that were obtained at one university in a state.