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
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section: Chapter Questions
Problem 5CR
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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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