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Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distri can be used, explain why. Interpret the results. In a random sample of 19 mortgage institutions, the mean interest rate was 3.43% and the standard deviation was 0.43%. Assume the interest rates are non distributed. Which distribution should be used to construct the confidence interval? OA. Use a normal distribution because n< 30 and the interest rates are normally distributed. DB. Use a t-distribution because it is a random sample, o is unknown, and the interest rates are normally distrihutod

Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distri can be used, explain why. Interpret the results. In a random sample of 19 mortgage institutions, the mean interest rate was 3.43% and the standard deviation was 0.43%. Assume the interest rates are non distributed. Which distribution should be used to construct the confidence interval? OA. Use a normal distribution because n< 30 and the interest rates are normally distributed. DB. Use a t-distribution because it is a random sample, o is unknown, and the interest rates are normally distrihutod

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Problem Statement:** Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 19 mortgage institutions, the mean interest rate was 3.43%, and the standard deviation was 0.43%. Assume the interest rates are normally distributed. **Question:** Which distribution should be used to construct the confidence interval? **Options:** A. Use a normal distribution because n < 30 and the interest rates are normally distributed. B. Use a t-distribution because it is a random sample, σ is unknown, and the interest rates are normally distributed. C. Use a t-distribution because the interest rates are normally distributed and σ is known. D. Use a normal distribution because the interest rates are normally distributed and σ is known. E. Cannot use the standard normal distribution or the t-distribution because σ is unknown, n < 30, and the interest rates are not normally distributed. **Answer:** Option B is the correct choice. Use a t-distribution because it is a random sample, σ is unknown, and the interest rates are normally distributed. **Explanation:** Since the sample size is less than 30 and the population standard deviation (σ) is unknown, the t-distribution is appropriate for constructing the confidence interval. The normal distribution can only be used if the population standard deviation is known or the sample size is sufficiently large.
Transcribed Image Text:**Problem Statement:** Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 19 mortgage institutions, the mean interest rate was 3.43%, and the standard deviation was 0.43%. Assume the interest rates are normally distributed. **Question:** Which distribution should be used to construct the confidence interval? **Options:** A. Use a normal distribution because n < 30 and the interest rates are normally distributed. B. Use a t-distribution because it is a random sample, σ is unknown, and the interest rates are normally distributed. C. Use a t-distribution because the interest rates are normally distributed and σ is known. D. Use a normal distribution because the interest rates are normally distributed and σ is known. E. Cannot use the standard normal distribution or the t-distribution because σ is unknown, n < 30, and the interest rates are not normally distributed. **Answer:** Option B is the correct choice. Use a t-distribution because it is a random sample, σ is unknown, and the interest rates are normally distributed. **Explanation:** Since the sample size is less than 30 and the population standard deviation (σ) is unknown, the t-distribution is appropriate for constructing the confidence interval. The normal distribution can only be used if the population standard deviation is known or the sample size is sufficiently large.
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