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In 2017, Americans spent a record-high $9.1 billion on Halloween-related purchases (the balance website). Sample data showing the amount, in dollars, 16 adults spent on a Halloween costume are as follows. 14 68 25 64 31 33 32 44 50 15 16 96 46 35 64 28 a. What is the estimate of the population mean amount adults spend on a Halloween costume (to 2 decimals)? $ b. What is the sample standard deviation (to 2 decimals)? $ c. Provide a 95% confidence interval estimate of the population standard deviation for the amount adults spend on a Halloween costume (to 2 decimals). Use Table 11.1. so≤8 $

In 2017, Americans spent a record-high $9.1 billion on Halloween-related purchases (the balance website). Sample data showing the amount, in dollars, 16 adults spent on a Halloween costume are as follows. 14 68 25 64 31 33 32 44 50 15 16 96 46 35 64 28 a. What is the estimate of the population mean amount adults spend on a Halloween costume (to 2 decimals)? $ b. What is the sample standard deviation (to 2 decimals)? $ c. Provide a 95% confidence interval estimate of the population standard deviation for the amount adults spend on a Halloween costume (to 2 decimals). Use Table 11.1. so≤8 $

MATLAB: An Introduction with Applications
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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In **2017**, Americans spent a record-high **$9.1 billion** on Halloween-related purchases (the *balance* website). Sample data showing the amount, in dollars **(16)** adults spent on a Halloween costume are as follows: 14, 68, 25, 64 31, 33, 32, 44 50, 15, 16, 96 46, 35, 64, 28 ### Questions: #### a. What is the estimate of the population mean amount adults spend on a Halloween costume (to 2 decimals)? \[ \text{Mean} = \$\_\_\_\_\_\_\_\_\_\_ \] #### b. What is the sample standard deviation (to 2 decimals)? \[ \text{Sample Standard Deviation} = \$\_\_\_\_\_\_\_\_\_\_ \] #### c. Provide a 95% confidence interval estimate of the population standard deviation for the amount adults spend on a Halloween costume (to 2 decimals). Use [Table 11.1](https://www.example.com). \[ \$\_\_\_\_\_\_\_\_ \leq \sigma \leq \$\_\_\_\_\_\_\_\_ \] ### Explanation of Data: - The data consists of **16** values, each representing the amount in dollars spent by different adults on a Halloween costume. - Values are arranged in a **4x4 grid** for better visualization and readability. Make sure to calculate accurately and refer to statistical techniques to find the mean, standard deviation, and confidence intervals.
Transcribed Image Text:In **2017**, Americans spent a record-high **$9.1 billion** on Halloween-related purchases (the *balance* website). Sample data showing the amount, in dollars **(16)** adults spent on a Halloween costume are as follows: 14, 68, 25, 64 31, 33, 32, 44 50, 15, 16, 96 46, 35, 64, 28 ### Questions: #### a. What is the estimate of the population mean amount adults spend on a Halloween costume (to 2 decimals)? \[ \text{Mean} = \$\_\_\_\_\_\_\_\_\_\_ \] #### b. What is the sample standard deviation (to 2 decimals)? \[ \text{Sample Standard Deviation} = \$\_\_\_\_\_\_\_\_\_\_ \] #### c. Provide a 95% confidence interval estimate of the population standard deviation for the amount adults spend on a Halloween costume (to 2 decimals). Use [Table 11.1](https://www.example.com). \[ \$\_\_\_\_\_\_\_\_ \leq \sigma \leq \$\_\_\_\_\_\_\_\_ \] ### Explanation of Data: - The data consists of **16** values, each representing the amount in dollars spent by different adults on a Halloween costume. - Values are arranged in a **4x4 grid** for better visualization and readability. Make sure to calculate accurately and refer to statistical techniques to find the mean, standard deviation, and confidence intervals.
### Table 11.1: Selected Values from the Chi-Square Distribution Table The provided Chi-Square Distribution Table (Table 11.1) is used primarily in statistical analyses to determine critical values of the chi-squared (χ²) distribution. These values are essential when performing tests such as the chi-square test for independence and the chi-square goodness of fit test. #### Diagram Overview The top part of the table includes a graphical representation of the chi-squared distribution, characterized by its asymmetrical shape, which skews to the right. Key points include: - **Degrees of Freedom (df)**: Located along the vertical axis. - **Area or Probability (α)**: Represented along the horizontal axis, indicating the area in the upper tail of the distribution. #### Table Breakdown The table below the graphical representation provides critical values for the chi-squared distribution across various degrees of freedom (df). Specific critical values are listed for different significance levels (α), including 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, and 0.01. ##### Degrees of Freedom vs. Area in Upper Tail | Degrees of Freedom | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 | 0.05 | 0.025 | 0.01 | |-------------------|-------|-------|-------|-------|-------|-------|-------|-------| | 1 | 0.000 | 0.001 | 0.004 | 0.016 | 2.706 | 3.841 | 5.024 | 6.635 | | 2 | 0.020 | 0.051 | 0.103 | 0.211 | 4.605 | 5.991 | 7.378 | 9.210 | | 3 | 0.115 | 0.216 | 0.352 | 0.584 | 6.251 | 7.815 | 9.348 | 11.345| | ... | ... | ... | ... | ... | ... | ... | ... | ... | | 10 | 2.558 | 3.247 | 3
Transcribed Image Text:### Table 11.1: Selected Values from the Chi-Square Distribution Table The provided Chi-Square Distribution Table (Table 11.1) is used primarily in statistical analyses to determine critical values of the chi-squared (χ²) distribution. These values are essential when performing tests such as the chi-square test for independence and the chi-square goodness of fit test. #### Diagram Overview The top part of the table includes a graphical representation of the chi-squared distribution, characterized by its asymmetrical shape, which skews to the right. Key points include: - **Degrees of Freedom (df)**: Located along the vertical axis. - **Area or Probability (α)**: Represented along the horizontal axis, indicating the area in the upper tail of the distribution. #### Table Breakdown The table below the graphical representation provides critical values for the chi-squared distribution across various degrees of freedom (df). Specific critical values are listed for different significance levels (α), including 0.99, 0.975, 0.95, 0.90, 0.10, 0.05, 0.025, and 0.01. ##### Degrees of Freedom vs. Area in Upper Tail | Degrees of Freedom | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 | 0.05 | 0.025 | 0.01 | |-------------------|-------|-------|-------|-------|-------|-------|-------|-------| | 1 | 0.000 | 0.001 | 0.004 | 0.016 | 2.706 | 3.841 | 5.024 | 6.635 | | 2 | 0.020 | 0.051 | 0.103 | 0.211 | 4.605 | 5.991 | 7.378 | 9.210 | | 3 | 0.115 | 0.216 | 0.352 | 0.584 | 6.251 | 7.815 | 9.348 | 11.345| | ... | ... | ... | ... | ... | ... | ... | ... | ... | | 10 | 2.558 | 3.247 | 3
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