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 95% confidence level. What does the confidence interval tell about the population of all college students in the state? 3.8, 3.0, 3.9, 4.4, 3.1, 4.3, 3.4, 4.7, 4.2, 4.2, 4.4, 3.8, 3.5, 4.2, 4.0 O What is the confidence interval for the population mean u? (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. O A. The results tell nothing about the population of all college students in the state, since the sample from only one university. O B. We are confident that 95% of all students gave evaluation ratings between and. (Round to one decimal place as needed.) O C. We are 95% confident that the interval from to actually contains the true mean evaluation rating. (Round to one decimal place as needed.)
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![### Student Evaluation Ratings Analysis
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 95% confidence level. What does the confidence interval tell about the population of all college students in the state?
**Ratings:**
3.8, 3.0, 3.9, 4.4, 3.1, 4.3, 3.4, 4.7, 4.2, 4.4, 3.8, 3.5, 4.2, 4.0
**Question 1:** What is the confidence interval for the population mean μ?
\[ \leq \mu \leq \] (Round to two decimal places as needed.)
**Question 2:** 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 confident that 95% of all students gave evaluation ratings between [ ] and [ ]. (Round to one decimal place as needed.)
- **C.** We are 95% confident that the interval from [ ] to [ ] actually contains the true mean evaluation rating. (Round to one decimal place as needed.)
[Option to select your answer(s).]
**Explanation:**
The text presents a typical problem of constructing a confidence interval for the mean from a sample of student evaluation ratings using a 95% confidence level. Additionally, the interpretation part guides students on how the confidence interval reflects on the population mean or the population ratings they are analyzing.
This type of exercise is designed to enhance understanding of statistical concepts and their application, particularly in educational assessments. By solving this, students practice how to calculate confidence intervals and interpret their meanings in context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77539088-565f-4afc-94a2-fa06d09c60a8%2Fc1cb606a-bab4-463f-9d1a-0d8d08d7c71b%2F9ly7777_processed.jpeg&w=3840&q=75)
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