I\'m doing a math project where I\'m doing a two proportion test I have to use r

Question

I'm doing a math project where I'm doing a two proportion test I have to use real data. I usd FBI statistics from  https://ucr.fbi.gov/crime-in-the-u.s/2015/crime-in-the-u.s.- 2015/tables/table-1. I want to get some feedback to see if this looks okay. I'm not sure if my work is correct or if i have the right data to do make a two proprtion test. Below is what I have.

Using data from the FBI I was able to find reports of the violent crime in the United States from the years 1996 to 2015 where I compared the number of people that experienced violent crime. My claim is that the same numbers of people experienced violent crime from their respective years. Claim: The proportion of victims that suffered from violent crime from the years 1996 is the same as for the year 2015 (p1=p2). False: The number of victims that suffered from violent crime is different from the year 1996 to 2015 (p1 p2).

P-Value < .05 Reject H0 The P-Value is less than .06 therefore we rejected H0. There is sufficient evidence to warrant rejection of the claim that the proportion of violent crime victims is the same form the years 1996 and 2015

H0: pl-pi Table 1 Violent Violent crime Year Population crime 1996 265,228,572 1,688,540 636.6 nl-265,228,572=1,688,540 1997 267,783,607 1,636,096 611.0 pl- 1,688,540/ 265,228,572006366 1998 270,248,003 1.533.887 1999272,690, 2000281,421,906 1.425,486 20015 285,317,559 1,439,480 2002 287,973,924 1,423,677 2003 290788.976 1.383,676 475.8 p 1,688,540 + 1,197,704/ 265,228,572 + 567.6 813 1,426,044 523.0 n2 = 321,418 ,820 X2= 1 , I 97,704 506.5 p2-1 , 197,704/ 321 ,418,820·003726 504.5 494.4 293.656,842 1,360,088 463.2 321,418,820 .004919 1004919-995081 2005 296,507,061 1,390,745 2006299,398,484 1.435,123 2007 301,621,157 1.422,970 2008 304,059,724 1,394.461 2009307,006,550 1,325,896 2010 309.330,219 1,251.248 2011 311,587,816 1.206,005 387.1 P-Value 0 2012 313,873,685 1,217,057 2013 316.497,531 1.168,298 2014 318,907,401 1,153,022 2015 321,418,820 1.197,704 469.0 479.3 471.8 Z=[(.006366-003 458 6.006366) (265228572 + 321418820 726)-01-V [.006366(1 1-400.14 4 265228572 321418820 431.9 Critical Z: +1.96, -1.96 404.5 387.8 369.1 361.6 372.6

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1 = P2
Alternative hypothesis: P1 P2

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.004919

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
S.E = 0.0000058

z = (p1 - p2) / SE

z = 437

zcritical = + 1.96

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -437 or greater than 437.

Thus, the P-value = 0

Interpret results. Since the P-value (0) is less than the significance level (0.05), we cannot accept the null hypothesis.

There is sufficient evidence to warrant rejection of the claim that the proportion of violent crime victims is the same form the years 1996 and 2015 .

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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