Questions to answer 1. For a t-distribution with 10 degrees of freedom, the prob

Questions to answer
1. For a t-distribution with 10 degrees of freedom, the probability covered within the interval of values [-2 to +2], is:
(Please use three decimal places (e.g., 0.345). Please do not enter your answer as a percentage.
2. For a Normal distribution, the probability covered within the interval [(mean – 2 x std. dev.) to (mean + 2 x std. dev.)], is:
(Please use three decimal places (e.g., 0.345). Please do not enter your answer as a percentage. ignore zeroes at the end, after the decimal place
3. Match the description of the estimator below (on the left) to the attribute (on the right): Unbiased, Inefficient, Inconsistence, Consistence, Biased, Efficient
a. Produces estimates with significant error (no matter the sample size)
b. Results in better estimates as the sample size increases.
c. Systematically underestimates or overestimates the population value.
The remaining questions pertain to a 99% Confidence Interval for the population mean of FICO score for *home improvement* purpose loans (please load the LendingClubLoanData.rds file in Radiant to answer this question).
For Questions 6-9, please enter values with three decimal places (e.g., 89.123).* Please note to ignore zeroes at the end, after the decimal place.
4. What is the sample size (n)?
5. The standardized sample mean in this case comes from a t-distribution with how many degrees of freedom?
6. What is the critical value (theta, or number of standard deviations on either side of the sample mean) to be used for calculating the lower and upper bounds of the confidence interval?
7. What is the margin of error?
8. What is the *lower bound* of the 99% Confidence Interval for the population mean of FICO score for *home improvement* loans?
To clarify, this question is *not asking* about the probability values that we enter in Radiant’s probability calculator.
9. What is the *upper bound* of the 99% Confidence Interval for the population mean of FICO score for *home improvement* loans?
To clarify, this question is *not asking* about the probability values that we enter in Radiant’s probability calculator.
10. Please read the one-pager “Additional Comments on Confidence Interval” available
Please select the correct interpretation of the Confidence Interval (CI) constructed above:
a. The probability that the population mean of FICO Score for home improvement loans falls within the constructed CI, is 99%.
b. If we draw samples of the same size repeatedly, 99% of the CIs constructed can be expected to include the population mean of FICO Score for home improvement loans.