2. Researchers know that the average rate of violence within intimate relationsh

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.

A. What are the independent and dependent variables and how are each scaled ?

            Independent:________________________            Scaling:_____________________________

            Dependent:__________________________            Scaling:_____________________________

B. What test should the students use?

E. What are that tests assumptions?  

H. If the researcherss calculate a test statistic of 1.78, should they?      Retain H0 Reject H0  

Explanation / Answer

Solution:-

A.

            Independent: Gender

            Dependent: Rate of violence.

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

Null hypothesis: = 20
Alternative hypothesis: 20

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean 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 one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 0.1517

z = (x - ) / SE

z = 21.09

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z statistic less than -21.09 or greater than 21.09.

Thus, the P-value = less than 0.0001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

H. If the researcherss calculate a test statistic of 1.78, then we should Retain H0

Since we have a two-tailed test, the P-value is the probability that the z statistic is less than -1.78 or greater than 1.78.

Thus, the P-value = 0.074

Interpret results. Since the P-value (0.074) is greater than the significance level (0.05), we have to accept the null hypothesis.

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