Is the national crime rate really going down Some sociologis

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. (Source: True Odds, by J. Walsh, Merritt Publishing.) Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 39 arrests last month, 22 were of males aged 15 to 34 years. Use a 5% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.

H_o: p 0.7; H₁: p = 0.7; two-tailedH_o: p = 0.7; H₁: p > 0.7; right-tailed    H_o: p = 0.7; H₁: p 0.7; two-tailedH_o: p =0 .7; H₁: p < 0.7; left-tailed

The normal distribution, since sample size is large.The t distribution, since the sample size is large.    

At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

Fail to reject the null hypothesis, there is insufficient evidence that the true proportion of arrests of males aged 14 to 34 in Rock Springs is different from 0.7.Fail to reject the null hypothesis, there is sufficient evidence that the true proportion of arrests of males aged 14 to 34 in Rock Springs is different from 0.7.    Reject the null hypothesis, there is insufficient evidence that the true proportion of arrests of males aged 14 to 34 in Rock Springs is different from 0.7.Reject the null hypothesis, there is sufficient evidence that the true proportion of arrests of males aged 14 to 34 in Rock Springs is different from 0.7.

Solution

1) 0.05

2) Two tailed test -

H₀ : p=0.7

H₁ : p =/= 0.7

3) Standard normal distribution.

Yes, sample is large enough because the sample size is greater than 30, hence central limit theorem holds and so sampling distribution would be normal.

4) -1.85

5) 0.0642

6) (C)

7) As p- value is greater than 0.05, so fail to reject null and conclude that the data is not statistically significant.

option (A) is correct.

8) Fail to reject the null hypothesis, there is insufficient evidence that the true proportion of arrests of males aged 14 to 34 in Rock Springs is different from 0.7.

Option (A)