If we want to be within 0.02 of the true proportion of homes that have a direct television receiver and have 98% confidence, how many do we need in our sample? It is believed that 82% of U.S. homes have a direct satellite television receiver. ### Educational Content on Sample Size and Proportions#### Questions and Exercises1. **Express as a Decimal Rounded to Two Decimal Places** - Task: Use the dropdown to select an answer and express it as a decimal rounded to two decimal places.2. **Express as a Decimal Rounded to Two Decimal Places** - Margin of Error: E - Task: Use the dropdown to select an answer and express it as a decimal rounded to two decimal places.3. **Express as a Decimal Rounded to Two Decimal Places** - Task: Use the dropdown to select an answer and express it as a decimal rounded to two decimal places.4. **Sample Size Calculation for Confidence Interval** - Scenario: If we want to be within 0.02 of the true proportion of homes that have a direct television receiver and have 98% confidence, how many do we need in our sample? - Assumption: It is believed that 82% of U.S. homes have a direct satellite television receiver. - Task: Use the dropdown to select an answer and round it to the next number.5. **Complete the Sentence with Proportional Requirements** - Goal: Write your numbers from least to greatest to complete the sentence. - Task: To be 98% confident and to be within 82%, the true proportion needs to be at least [blank].#### ExplanationThis exercise helps you understand how to calculate and round proportions and sample sizes for statistical analysis. It also emphasizes statistical confidence levels and margins of error, which are critical in determining appropriate sample sizes for surveys.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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If we want to be within 0.02 of the true proportion of homes that have a direct television receiver and have 98% confidence, how many do we need in our sample? It is believed that 82% of U.S. homes have a direct satellite television receiver.

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The population proportion is 82%, the confidence level is 98% and estimate is within 0.02.

Computation of critical value:

$\begin{array}{rcl} (1 - α) & = & 0.98 \\ α & = & 0.02 \\ \frac{α}{2} & = & 0.01 \\ 1 - \frac{α}{2} & = & 0.99 \end{array}$

The critical value of z-distribution can be obtained using the excel formula “=NORM.S.INV(0.99)”. The critical value is 2.3263.

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