Is the crime rate in New York different from the crime rate in New Jersey? Independent random samples from region A (cities in New York) and region B (cities in New Jersey) gave the following information about violent crime rate (number of violent crimes per 100,000 population). (Reference: U.S. Department of Justice, Federal Bureau of Investigation.)
Use a 10% level of significance to test the claim that there is no difference in the crime rate distributions of the two states.
(a) What is the level of significance?
State the null and alternate hypotheses.
Ho
: Distributions are different.H1
: Distributions are the same.Ho
: Distributions are the same.H1
: Distributions are different.Ho
: Distributions are the same.H1
: Distributions are the same.Ho
: Distributions are different.H1
: Distributions are different.
(b) Compute the sample test statistic. (Use 2 decimal places.)
What sampling distribution will you use?
chi-squareStudent'st normaluniform
What conditions are necessary to use this distributions?
Both sample sizes must be less than 10.At least one sample size must be less than 10. Both sample sizes must be greater than 10.At least one sample size must be greater than 10.
(c) Find the
P-value of the sample test statistic. (Use 4 decimal places.)
(d) Conclude the test?
At the ? = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.
Fail to reject the null hypothesis, there is sufficient evidence that the crime rate distributions differ.Fail to reject the null hypothesis, there is insufficient evidence that the crime rate distributions differ. Reject the null hypothesis, there is sufficient evidence that the crime rate distributions differ.Reject the null hypothesis, there is insufficient evidence that the crime rate distributions differ.