(11 points)
NYC Restaurant Employees ~ Restaurants are one of the key elements that make New York City a world-class metropolis. Vibrant restaurants draw concentrations of retail, arts, and entertainment to the city, and they imbue neighborhoods with character and individuality.In 2018, the U.S. Census Bureau conducted a study on the demographics of restaurant workers in NYC. The percentage distribution of race/ethnicity from this study is reported in the table below.Alberto is a recent graduate who majored in hotel management and hospitality. He wants to determine if the distribution of restaurant workers by race and ethnicity in NYC has changed from 2018. Alberto conducts a survey of 580 employees of the restaurant industry within NYC and records their race/ethnicity. These values are also shown in the table.
| Race/Ethnicity | 2018 Percentage | Sample Results |
| Hispanic | 43.9% | 256 |
| White | 21.8% | 123 |
| Asian | 18.9% | 116 |
| Black | 13.5% | 69 |
| Other | 1.9% | 16 |
| Total | 100% | 580 |
Round all calculated answers to 4 decimal places.1. What type of hypothesis test should Alberto use to answer his research question?
A. ????2?2 goodness of fit test
B. One-sample z-test for a population proportion
C. ????2?2 test of independence
D. One-sample bootstrap test for a population proportion
E. Two-sample randomization test for the difference in population proportions
2. Choose from the dropdown menus to complete the null and alternative hypotheses Alberto should use to conduct the hypothesis test.
????0H0: The distribution of race/ethnicity in restaurant employees in New York City is ? smaller than larger than the same as different from the percentages reported by the Census Bureau in 2018. Any observed difference ? is is not due to chance.????????Ha: The distribution of race/ethnicity in restaurant employees in New York City is ? smaller than larger than the same as different from the percentages reported by the Census Bureau in 2018.
3. What conditions must be met for the hypothesis test to be valid?
A. There must be an expected count of at least 5 for each level of the categorical variable.
B. There must be at least 10 'success' and 10 'failure' observations in each level of the categorical variable.
C. The difference in percentages must be greater than or equal to the p-value.
D. Each observation must be independent of all other observations.
E. There must be at least 3 levels of the categorical variable.
4. Calculate the expected count for the number of restaurant employees you would expect in the category, “Other”, under the null hypothesis.
Expected count for “Other” =
5. Calculate the contribution toward the test statistic from the category “Other”.
Contribution =
6. Calculate the test statistic for this test.
????2 =
7. State the degrees of freedom for this test.
????????=
7. Calculate the p-value.
p-value =
8. How much evidence does Diana have against the null hypothsis?
A. Little
B. Some
C. Strong
D. Very Strong
E. Extremely Strong