Math Problem Statement

According to the Census​ Bureau, 18.1​% of the people in the United States are of Hispanic or Latino origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey​ data, which was a random sample of 421 county​ residents, and found that 53 of those surveyed are of Hispanic origin. Complete parts​ (a) through​ (d) below. Question content area bottom Part 1 ​a) State the hypotheses. Let the proportion of people in the county that are of Hispanic origin be denoted by p. Choose the correct answer below. A.Upper H 0 : p greater than or equals 0.181 Upper H Subscript Upper A Baseline : p less than 0.181 Upper H 0 : p greater than or equals 0.181 Upper H Subscript Upper A Baseline : p less than 0.181 B.Upper H 0 : p less than 0.181 Upper H Subscript Upper A Baseline : p equals 0.181 Upper H 0 : p less than 0.181 Upper H Subscript Upper A Baseline : p equals 0.181 C.Upper H 0 : p equals 0.181 Upper H Subscript Upper A Baseline : p not equals 0.181 Upper H 0 : p equals 0.181 Upper H Subscript Upper A Baseline : p not equals 0.181 Your answer is correct.D.Upper H 0 : p equals 0.181 Upper H Subscript Upper A Baseline : p less than 0.181 Upper H 0 : p equals 0.181 Upper H Subscript Upper A Baseline : p less than 0.181 Part 2 ​b) Name the model and check appropriate conditions for a hypothesis test. What kind of test is​ this? Difference in differences test ​Two-proportion t test ​One-proportion z test Your answer is correct. Proportional t test Part 3 Check the appropriate conditions for a hypothesis test. Select the correct choice below and fill in the answer boxes within your choice. ​(Round to one decimal place as​ needed.) A. The 421 residents were a random sample from the county of interest. 421 is likely less than​ 10% of the population of a county. One expects np 0equals    enter your response here successes and nq 0equals    enter your response here ​failures, which are both more than 10. B. The 421 residents were a random sample from the county of interest. The sample size is more than 100. One expects np 0equals    enter your response here successes and nq 0equals    enter your response here ​failures, which are both more than 10. C. The 421 residents were a random sample from the county of interest. The standard deviation of p is less than 0.5. One expects np 0equals    enter your response here successes and nq 0equals    enter your response here ​failures, which are both more than 20.

Solution

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Proportions
One-Proportion Z-Test

Formulas

Z-test formula for proportion: z = (p̂ - p0) / √(p0 * (1 - p0) / n)

Theorems

Central Limit Theorem

Suitable Grade Level

College Level (Statistics Course)