Question

Listed bolow are student evaluation ratings of courses, where a rating of 5 is for "excellont." The ratings were obtained at one univorsity in a state. Censtruct a confidence interval using a 98% confidence lovel. What does the confidence interval tell abcet the populabion of all college students in the state? 39,3,1,37,48,30,43,3,5,49,46,4.0,43,3,7,3.6,39,3.6=

What is the corfidence interval for the popidation mean p?

Answer 1

A confidence interval is constructed to estimate the population mean rating of courses for all college students in the state.

Step-by-step explanation:

A confidence interval is a range of values that is likely to contain the true population parameter. In the case of this study, a confidence interval is constructed to estimate the population mean rating of courses for all college students in the state.

To construct a confidence interval, we need to calculate the mean and standard deviation of the sample ratings. Using the provided data, the mean is 22.74 and the standard deviation is 17.59. With a 98% confidence level, we can use the t-distribution to determine the margin of error.

The confidence interval can be calculated as follows:

Margin of error = t-value * (standard deviation / sqrt(sample size))

t-value for a 98% confidence level with 16 degrees of freedom is approximately 2.583.

Substituting the values into the formula:

Margin of error = 2.583 * (17.59 / sqrt(18)) = 15.39

Therefore, the confidence interval for the population mean rating is approximately (7.35, 38.13).