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MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Confidence Interval Estimation for Delivery Time of Tax Forms**

Suppose that an accounting firm conducts a study to determine the time needed to complete one person's tax forms. It surveys 200 people randomly. The sample mean observed is 23.1 hours, and there is a known population standard deviation of 6.4 hours. The population distribution is assumed to be normal.

**Note:** If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. However, you must first prove this assumption.

**Constructing a 90% Confidence Interval:**

1. **State the Confidence Interval:**
   - Interval: [22.36, 23.84] (rounded to two decimal places).

2. **Graph Explanation:**
   - The graph displays a standard normal distribution curve centered around the sample mean.
   - The confidence level (C.L.) is shown in the center of the curve.
   - The left and right tails of the curve, marked by arrows, represent the critical values \( \frac{\alpha}{2} \).

3. **Calculate the Error Bound:**
   - Error bound (E): (This part requires calculation.)

This interval estimation captures the mean time needed with a 90% confidence level, taking into account sample variability.
Transcribed Image Text:**Confidence Interval Estimation for Delivery Time of Tax Forms** Suppose that an accounting firm conducts a study to determine the time needed to complete one person's tax forms. It surveys 200 people randomly. The sample mean observed is 23.1 hours, and there is a known population standard deviation of 6.4 hours. The population distribution is assumed to be normal. **Note:** If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. However, you must first prove this assumption. **Constructing a 90% Confidence Interval:** 1. **State the Confidence Interval:** - Interval: [22.36, 23.84] (rounded to two decimal places). 2. **Graph Explanation:** - The graph displays a standard normal distribution curve centered around the sample mean. - The confidence level (C.L.) is shown in the center of the curve. - The left and right tails of the curve, marked by arrows, represent the critical values \( \frac{\alpha}{2} \). 3. **Calculate the Error Bound:** - Error bound (E): (This part requires calculation.) This interval estimation captures the mean time needed with a 90% confidence level, taking into account sample variability.
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