d. The degrees of freedom = e. The test-statistic for this data show your answer to three decimal places.) f. The p-value for this sample your answer to four decimal places.) = = (Please (Please show

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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A recent report shows that 24.2% of all Americans prefer vanilla ice cream, 23.3% prefer chocolate, 9.6% favor butter pecan, 9.4% favor strawberry, and the rest have other favorites. An ice cream shop owner believes her customers differ from the general American preferences. The results from 790 of her patrons’ ice cream choices are shown below. A statistical analysis at a 0.01 significance level seeks to determine if her customers' preferences align with national trends.

### Table: Frequencies of Favorite Ice Cream

| Outcome      | Frequency | Expected Frequency |
|--------------|-----------|--------------------|
| Vanilla      | 184       |                    |
| Chocolate    | 183       |                    |
| Butter Pecan | 68        |                    |
| Strawberry   | 69        |                    |
| Other        | 286       |                    |

### Statistical Analysis

#### a. Complete the table by calculating expected frequencies.
*Round the expected frequencies to the nearest whole number.*

#### b. Appropriate Statistical Test
- **Goodness-of-Fit Test** ✓

#### c. Null and Alternative Hypotheses

**\( H_0 \):**  
The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general. ✓

**\( H_1 \):**  
The null hypothesis is not specified in detail in the image but should represent the opposite case to \( H_0 \).

This setup aims to determine if the shop's customer preferences significantly deviate from the national statistics using a chi-square goodness-of-fit test.
Transcribed Image Text:A recent report shows that 24.2% of all Americans prefer vanilla ice cream, 23.3% prefer chocolate, 9.6% favor butter pecan, 9.4% favor strawberry, and the rest have other favorites. An ice cream shop owner believes her customers differ from the general American preferences. The results from 790 of her patrons’ ice cream choices are shown below. A statistical analysis at a 0.01 significance level seeks to determine if her customers' preferences align with national trends. ### Table: Frequencies of Favorite Ice Cream | Outcome | Frequency | Expected Frequency | |--------------|-----------|--------------------| | Vanilla | 184 | | | Chocolate | 183 | | | Butter Pecan | 68 | | | Strawberry | 69 | | | Other | 286 | | ### Statistical Analysis #### a. Complete the table by calculating expected frequencies. *Round the expected frequencies to the nearest whole number.* #### b. Appropriate Statistical Test - **Goodness-of-Fit Test** ✓ #### c. Null and Alternative Hypotheses **\( H_0 \):** The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general. ✓ **\( H_1 \):** The null hypothesis is not specified in detail in the image but should represent the opposite case to \( H_0 \). This setup aims to determine if the shop's customer preferences significantly deviate from the national statistics using a chi-square goodness-of-fit test.
Certainly! Here's the transcribed text as it might appear on an educational website:

---

### Statistical Analysis Exercise

**d.** The degrees of freedom = [__________]

**e.** The test-statistic for this data = [__________] 
*(Please show your answer to three decimal places.)*

**f.** The p-value for this sample = [__________] 
*(Please show your answer to four decimal places.)*

---

#### Explanation

In this exercise, students are required to calculate and enter the following statistical values:

- **Degrees of Freedom**: A parameter used in various statistical analyses that reflects the number of values in a calculation that are free to vary.

- **Test-Statistic**: A value calculated from a statistical test. Students are asked to round their answer to three decimal places.

- **P-Value**: The probability of obtaining test results at least as extreme as the observed results under the null hypothesis. Answers should be presented to four decimal places.

These concepts are crucial in determining the significance of the data and understanding how to interpret statistical results.

---
Transcribed Image Text:Certainly! Here's the transcribed text as it might appear on an educational website: --- ### Statistical Analysis Exercise **d.** The degrees of freedom = [__________] **e.** The test-statistic for this data = [__________] *(Please show your answer to three decimal places.)* **f.** The p-value for this sample = [__________] *(Please show your answer to four decimal places.)* --- #### Explanation In this exercise, students are required to calculate and enter the following statistical values: - **Degrees of Freedom**: A parameter used in various statistical analyses that reflects the number of values in a calculation that are free to vary. - **Test-Statistic**: A value calculated from a statistical test. Students are asked to round their answer to three decimal places. - **P-Value**: The probability of obtaining test results at least as extreme as the observed results under the null hypothesis. Answers should be presented to four decimal places. These concepts are crucial in determining the significance of the data and understanding how to interpret statistical results. ---
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