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 99% confidence level. What does the confidence interval tell about the population of all college students in the state?

3.6, 3.1, 4.0, 4.9, 3.0, 4.3, 3.6, 4.6, 4.6, 4.0, 4.4, 3.6, 3.3, 4.2, 3.7

What is the confidence interval for the population mean mu?

_ < u < _

nothing (Round to two decimal places as needed.)

3.49 < u < 4.37

Step-by-step explanation:

Data provided

3.6, 3.1, 4.0, 4.9, 3.0, 4.3, 3.6, 4.6, 4.6, 4.0, 4.4, 3.6, 3.3, 4.2, 3.7

The sample mean and deviation can be calculated with the following formulas

represent the sample mean

population mean

s=0.574 represent the sample standard deviation

n=15 represent the sample size  

Confidence interval

The confidence interval for the true mean is given by:

  (1)

The degrees of freedom, given by:

The Confidence is 0.99 or 99%, the significance is and , and the critical value would be

Replacing we got:

3.49 < u < 4.37

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is: