random sample is selected from an approximately normal population
with unknown standard deviation. Find the degrees of freedom and
the critical t value t∗ for the
given sample size and confidence level. Round critical t values to
4 decimal places.
- 1 Identify The Critical T An Independent Random Sample Is Selected From An Approximately Normal Population With Unknow 1 (15.61 KiB) Viewed 74 times
union that serves a large, urban area. For his annual report, he
wants to estimate the mean interest rate for 60-month fixed-rate
auto loans at lending institutions (banks, credit unions, auto
dealers, etc.) in his area. George selects a random sample of 12
lending institutions and obtains the following rates:
Round all calculated answers to 4 decimal places. George
calculates a sample mean of 5.2508 and a sample standard deviation
of 2.3645.1. Calculate a 95% confidence
interval for the mean interest rate for 60-month fixed-rate auto
loans at lending institutions in George’s area. Assume necessary
conditions have been met and round your result to 4 decimal
places.
2. ( , )
After calculating the interval, George decides he wants to
estimate the interest rate for 60-month fixed-rate auto loans at
95% confidence with a margin of error of no more than 0.48.
Using George’s initial sample results as a starting point, how
large a sample would George need to collect to accomplish his goal?
Use a t∗ value rounded to 3 decimal places in your
calculations and give your answer as an integer.
3. n =
?
3. George's colleague Rachel works at a
credit union in a different city. Rachel collects a similar sample
from her city and calculates a 90% confidence interval of (4.7162,
6.189). Which of the following statements are correct
interpretations of Rachel's interval?
A. If Rachel collected another sample, there
is a 90% chance that her new sample mean would be between 4.7162
and 6.189.
B. Rachel can be 90% confident that the true
mean 60-month fixed-rate auto loans interest rate in her city is
between 4.7162 and 6.189.
C. 90% of all lending institutions in
Rachel's city have a 60-month fixed-rate auto loans interest rate
between 4.7162 and 6.189.
D. There is a 90% chance that Rachel's sample
mean is between 4.7162 and 6.189.
E. If Rachel collected 100 random samples and
constructed a 90% confidence interval from each sample using the
same method, she could expect that approximately 90% of the
intervals would include the true mean.
4. If Rachel calculated a 95% confidence
interval instead, that interval would be (wider
than, narrower than, the same width) as her 90%
interval of (4.7162, 6.189).
Sample size, n Confidence level Degrees of Freedom Critical value, t* 4 90 25 95 23 98 19 99