I’m working on a statistics question and need an explanation to help me learn.
1. Use the appropriate t-distribution function to answer the following questions. In your answer, please note the function used and the arguments along with the answer (e.g. using T.INV.2T(0.05, 16) = 2.12.
a. 99% of the values in a t distribution with 18 degrees of freedom will be less than or equal to ______.
b. 1% of the values in a t distribution with 10 degrees of freedom will be greater than _____.
c. 95% of the values in a t distribution with 14 degrees of freedom will be in the interval -_____ to +_____ around the center of the distribution.
d. In a t distribution with 10 degrees of freedom, the probability that t is less than 1.5 is _____%.
e. In a t distribution with 25 degrees of freedom, the probability that t is greater than 2 is _____%.
2. Consider the variable “number living together.”
a. What is the mean number of people living together off-campus?
b. What is the median number of people living together?
c. What is the standard deviation of the number of people living together?
d. Create a 95% confidence interval for the average number of people living together.
e. Fully interpret the interval: what exactly does it tell you?
3. This question concerns the variable “individual rent,” which represents the individual’s share of the rent paid for off-campus housing. Note that many survey respondents did not report their individual rent.
a. How many students in the survey reported the rent that they pay individually?
b. What are the minimum and maximum individual rents paid by students in the sample?
c. What is the average individual rent?
d. What is the standard deviation of the rent?
e. What percentage of survey respondents left this question blank? Is the fact that some students chose not to answer the question likely to bias the mean upward, downward, or not in any particular direction? Explain your answer.
4. This question asks you to consider the average cost of living off-campus.
a. Build a 95% confidence interval for the mean rent paid individually by off-campus students.
b. Use your answer to estimate how much a student living off-campus should budget each year for rent. Explain your answer.