Math Problem Statement

In​ 2016, the Centers for Disease Control and Prevention reported that 36.5​% of adults in the United States are obese. A county health service planning a new awareness campaign polls a random sample of 600 adults living there. In this​ sample, 186 people were found to be obese based on their answers to a health questionnaire. Do these responses provide strong evidence that the 36.5​% figure is not accurate for this​ region? Correct the mistakes you find in the accompanying​ student's attempt to test an appropriate hypothesis. Consider an event to be rare if its probability of occurring is less than 0.05. LOADING... Click the icon to view the​ student's attempt to test an appropriate hypothesis. Question content area bottom Part 1 In the following​ calculations, enter the values from the​ student's attempt if they are correct. If the values from the​ student's attempt are​ incorrect, replace them with the correct values that most closely align with the​ student's attempt. Identify the hypotheses. Let any proportion refer to the proportion of adults who are obese. Upper H 0​: p equals

0.365 Upper H Subscript Upper A​: p #38 ne

0.365 ​(Type integers or decimals. Do not​ round.) Part 2 Check the Independence Assumption and the Randomization Condition. Select the correct choice​ and, if​ necessary, fill in the answer box to complete your choice. ​(Round to the nearest integer as​ needed.) A. These are satisfied because npequals

enter your response heregreater than or equals10 and nqequals

enter your response heregreater than or equals10. B. These are satisfied because npequals

enter your response hereless than or equals10 and nqequals

enter your response hereless than or equals10. C. These are satisfied because nequals

enter your response heregreater than​10% of the county population. D. These are both egregiously violated. E. These are satisfied because the sample was a simple random sample. F. These are satisfied because nequals

enter your response hereless than​10% of the county population. Upper H 0:Click the icon to view the student's attempt to test an appropriate hypothesis.Click the icon to view the student's attempt to test an appropriate hypothesis.Upper H Subscript Upper AUpper H Subscript Upper A:Click the icon to view the student's attempt to test an appropriate hypothesis.Click the icon to view the student's attempt to test an appropriate hypothesis.(Type integers or decimals. Do not round.)))))))) Help me solve this View an example Get more help pop-up content starts Student's Attempt Upper H 0​: ModifyingAbove p with caretequals0.365 Upper H Subscript Upper A​: ModifyingAbove p with caretless than0.365 ​SRS, 600greater than or equals10 StartFraction 186 Over 600 EndFraction equals0.310​; SD left parenthesis ModifyingAbove p with caret right parenthesisequalsStartRoot StartFraction left parenthesis 0.310 right parenthesis left parenthesis 0.690 right parenthesis Over 600 EndFraction EndRoot equals0.0189 zequalsStartFraction 0.310 minus 0.365 Over 0.0189 EndFraction equalsnegative 2.91 PequalsUpper P left parenthesis z greater than minus 2.91 right parenthesisequals0.998 There is more than a 99.8​% chance that the stated percentage is correct for this region. pop-up content ends

Solution

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Proportions
Z-Test
Statistical Significance

Formulas

Sample proportion (p̂) = x/n
Standard deviation of sample proportion: SD(p̂) = sqrt[(p(1 - p))/n]
Z-score formula: z = (p̂ - p) / SD(p̂)

Theorems

Central Limit Theorem
Normal Approximation for Proportions

Suitable Grade Level

Grades 11-12 or College Statistics