A report just came out that stated that 21.9% of all Americans say that vanilla is their favorite ice cream, 23.8% say that chocolate is their favorite, 9.6% favor butter pecan, 9.1% favor strawberry, and the rest have other favorites. An ice cream shop owner thinks that her customers are not like the rest of America. The table below shows the results of 775 of her patrons' ice cream selections. What can be concluded at the a = 0.01 significance level? a. Complete the table by filling in the expected frequencies. Round your answers to the nearest whole number. Frequencies of Favorite Ice Cream Outcome Frequency Expected Frequency Vanilla 156 Chocolate 184 Butter Pecan 68 Strawberry 72 Other 295 b. What is the correct statistical test to use? Select an answer ✓ c. What are the null and alternative hypotheses? Ho: Favorite ice cream and where the ice cream is purchased are dependent. O Favorite ice cream and where the ice cream is purchased are independent. O The distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general. The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general.

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### Research Hypothesis Testing: Ice Cream Preference

**Hypothesis (H1):**

- The hypothesis choices are as follows:
  - The distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general.
  - Favorite ice cream and where the ice cream is purchased are independent.
  - The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general.
  - Favorite ice cream and where the ice cream is purchased are dependent.

**Statistical Analysis Steps:**

**d. Degrees of Freedom:**
   - Input required: A numerical value that indicates the number of degrees of freedom for the data.

**e. Test Statistic:**
   - Input required: Calculate the test statistic for the data and enter the value to three decimal places.

**f. P-value:**
   - Input required: Compute the p-value for the sample and enter the value to four decimal places.

**g. P-value Comparison:**
   - Decision point to compare the p-value to the significance level (α).

**h. Decision:**
   - Based on the comparison, determine if the null hypothesis should be rejected or not.

**i. Conclusion:**
   - Choose the final conclusion based on the statistical test:
     - Sufficient evidence that the distribution of favorite ice cream is not the same as for Americans in general.
     - Sufficient evidence that favorite ice cream and purchase location are dependent.
     - Insufficient evidence that favorite ice cream and purchase location are dependent.
     - Sufficient evidence that the distribution of favorite ice cream is the same as for Americans in general.
     - Insufficient evidence that the distribution of favorite ice cream is not the same as for Americans in general.

This exercise involves completing the statistical analysis process by entering the appropriate values and making a conclusion based on evidence from the hypothesis test.
Transcribed Image Text:### Research Hypothesis Testing: Ice Cream Preference **Hypothesis (H1):** - The hypothesis choices are as follows: - The distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general. - Favorite ice cream and where the ice cream is purchased are independent. - The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general. - Favorite ice cream and where the ice cream is purchased are dependent. **Statistical Analysis Steps:** **d. Degrees of Freedom:** - Input required: A numerical value that indicates the number of degrees of freedom for the data. **e. Test Statistic:** - Input required: Calculate the test statistic for the data and enter the value to three decimal places. **f. P-value:** - Input required: Compute the p-value for the sample and enter the value to four decimal places. **g. P-value Comparison:** - Decision point to compare the p-value to the significance level (α). **h. Decision:** - Based on the comparison, determine if the null hypothesis should be rejected or not. **i. Conclusion:** - Choose the final conclusion based on the statistical test: - Sufficient evidence that the distribution of favorite ice cream is not the same as for Americans in general. - Sufficient evidence that favorite ice cream and purchase location are dependent. - Insufficient evidence that favorite ice cream and purchase location are dependent. - Sufficient evidence that the distribution of favorite ice cream is the same as for Americans in general. - Insufficient evidence that the distribution of favorite ice cream is not the same as for Americans in general. This exercise involves completing the statistical analysis process by entering the appropriate values and making a conclusion based on evidence from the hypothesis test.
## Ice Cream Preferences Statistical Analysis

A recent report indicates that 21.9% of all Americans prefer vanilla ice cream, 23.8% prefer chocolate, 9.6% favor butter pecan, 9.1% choose strawberry, and the remainder have other favorites. An ice cream shop owner suspects her patrons' preferences differ from the national average. The table below illustrates the results from 775 of her customers. We'll analyze this data at a 0.01 significance level.

### Table of Frequencies of Favorite Ice Cream

| Outcome      | Frequency | Expected Frequency |
|--------------|-----------|--------------------|
| Vanilla      | 156       |                    |
| Chocolate    | 184       |                    |
| Butter Pecan | 68        |                    |
| Strawberry   | 72        |                    |
| Other        | 295       |                    |

1. **Complete the Table**: Calculate the expected frequencies based on national preferences and fill in the corresponding fields. Round these values to the nearest whole number.

2. **Select Statistical Test**: Determine the correct statistical test to evaluate the hypothesis.
   - Options include:
     - Chi-square test of independence
     - Chi-square goodness of fit

3. **Hypotheses Definition**:
   - **Null Hypothesis (H₀)**:
     - The distribution of favorite ice cream flavors for customers at her shop is the same as the national distribution.
   - **Alternative Hypothesis (H₁)**:
     - The distribution of favorite ice cream flavors for customers at her shop is not the same as the national distribution.

By completing this analysis, we can conclude whether there's a significant difference between the shop's customer preferences and those of the general American population.
Transcribed Image Text:## Ice Cream Preferences Statistical Analysis A recent report indicates that 21.9% of all Americans prefer vanilla ice cream, 23.8% prefer chocolate, 9.6% favor butter pecan, 9.1% choose strawberry, and the remainder have other favorites. An ice cream shop owner suspects her patrons' preferences differ from the national average. The table below illustrates the results from 775 of her customers. We'll analyze this data at a 0.01 significance level. ### Table of Frequencies of Favorite Ice Cream | Outcome | Frequency | Expected Frequency | |--------------|-----------|--------------------| | Vanilla | 156 | | | Chocolate | 184 | | | Butter Pecan | 68 | | | Strawberry | 72 | | | Other | 295 | | 1. **Complete the Table**: Calculate the expected frequencies based on national preferences and fill in the corresponding fields. Round these values to the nearest whole number. 2. **Select Statistical Test**: Determine the correct statistical test to evaluate the hypothesis. - Options include: - Chi-square test of independence - Chi-square goodness of fit 3. **Hypotheses Definition**: - **Null Hypothesis (H₀)**: - The distribution of favorite ice cream flavors for customers at her shop is the same as the national distribution. - **Alternative Hypothesis (H₁)**: - The distribution of favorite ice cream flavors for customers at her shop is not the same as the national distribution. By completing this analysis, we can conclude whether there's a significant difference between the shop's customer preferences and those of the general American population.
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