Question

2. Researchers know that the average rate of violence within intimate relationships is 20 men or women per minute in the US (SD=2.47), according to the National Coalition against Domestic Violence (NCADV). The local chapter of the NCADV is concerned about area rates of domestic violence because the local average is 23.20 (N=265). They would like to determine if the local rate is the same as the national rate. (Total 29 pts)

A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)?

   Independent:________________________   Scaling:_____________________________

   Dependent:__________________________   Scaling:_____________________________

B. What test should be used (4 pts)?__________________________________________________

C. Why that test (2 pts)?

D. What are the null and alternative hypotheses for that test (4 pts)?

E. What are that tests assumptions (3 pts)?

F. What are the df (2 pts)?________________________

G. What is the critical value for p=.05 (2 pts)? _________________________

H. If the researchers calculate a test statistic of 1.78, should they (2 pts)?     Retain H0       Reject H0

I. Interpret the findings (6 pts):

Answer 1

A. Independent variable: Relationship

Scaling - Interval

Dependent variable: Domestic violence

scaling - Interval

B. We should use a Z test for testing.

C. We should use a Z test because the sample size is sufficiently large and the population standard deviation is known.

D. Null and alternative hypothesis.

E. Assumptions:

1) The sample should come from a normal population with known standard deviation.

2) The sample should be a random sample.

3) The scale measurement of the variable should be interval or ratio.

F. DF = N - 1 = 265 - 1 = 264

G. Here the test is a two-tailed test since the alternative hypothesis contains not equal to sign.

p that is alpha = 0.05

alpha/2 = 0.025 => 1 - (alpha/2) = 0.975

By using z table the z critical value for area 0.975 is 1.96

That is there are 2 critical values for a two-tailed test both are same just opposite in sign which is +1.96 and -1.96

H. If the test statistics is 1.78 which is between -1.96 and +1.96 so we retain the null hypothesis(H0)

I. We retain the null hypothesis that is researcher claim is correct that is the average rate of violence within an intimate relationship is 20 men or women per minute in the US.