2. A five-year-old census recorded that 20% of the families in a large community

Question

2. A five-year-old census recorded that 20% of the families in a large community lived below the poverty level. To determine if this percentage has changed, a random sample of 400 families is studied and 70 are found to be living below the poverty level. Does this finding indicate that the current percentage of families earning incomes below the poverty level has changed from what it was five years ago? Test with =0.05.

(a) Formulate the null and the alternative hypothesis.

(b) State and calculate the test statistics from the data.

You can use calculator, but all formulas (with numbers) have to be presented

(c) Calculate the P-value.

(d) Draw a conclusion in full sentence in the context of this problem (to write Reject of Fail to Reject the Null Hypothesis IS NOT ENOUGH)

Please show your work to help me understand, thank you.

Explanation / Answer

Data:    

n = 400   

p = 0.2   

p' = 70/400 = 0.175   

Hypotheses:    

Ho: p = 0.2   

Ha: p 0.2   

Decision Rule:    

= 0.05   

Lower Critical z- score = -1.9600   

Upper Critical z- score = 1.9600   

Reject Ho if |z| > 1.9600   

Test Statistic:    

SE = {p (1 - p)/n} = (0.2 * (1 - 0.2)/400) = 0.0200

z = (p'- p)/SE = (0.175 - 0.2)/0.02 = -1.2500

p- value = 0.2113   

Decision (in terms of the hypotheses):    

Since 1.2500 < 1.9600 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that p 0.2

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.