Reference no: EM133051394
Auto Loans: George works for a credit 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:
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2.83
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3.17
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5.79
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3.93
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5.37
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5.63
|
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3.88
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2.64
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4.48
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5.33
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2.48
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5.22
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Round all calculated answers to 4 decimal places.George calculates a sample mean of 4.2292 and a sample standard deviation of 1.237.
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.( , )
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 0.24.
2. 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∗t∗ value rounded to 3 decimal places in your calculations and give your answer as an integer.n=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 99% confidence interval of (3.4421, 6.0846). Which of the following statements are correct interpretations of Rachel's interval?
A. 99% of all lending institutions in Rachel's city have a 60-month fixed-rate auto loans interest rate between 3.4421 and 6.0846.
B. There is a 99% chance that Rachel's sample mean is between 3.4421 and 6.0846.
C. Rachel can be 99% confident that the true mean 60-month fixed-rate auto loans interest rate in her city is between 3.4421 and 6.0846.
D. If Rachel collected another sample, there is a 99% chance that her new sample mean would be between 3.4421 and 6.0846.
E. If Rachel collected 100 random samples and constructed a 99% confidence interval from each sample using the same method, she could expect that approximately 99% of the intervals would include the true mean.
4. If Rachel calculated a 90% confidence interval instead, that interval would be ? wider than narrower than the same width as her 99% interval of (3.4421, 6.0846).
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