SOLUTION: p Value? 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. I

Question 1077934: p Value?
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�. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 35 arrests last month, 29 were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.
(a) What is the level of significance?

.01

Correct: Your answer is correct.

State the null and alternate hypotheses.
H0: p < 0 .7; H1: p = 0.7
H0: p = 0 .7; H1: p < 0.7
H0: p = 0.7; H1: p ≠ 0.7
H0: p = 0.7; H1: p > 0.7
H0: p ≠ 0.7; H1: p = 0.7
Correct: Your answer is correct.
(b) What sampling distribution will you use?
The Student's t, since np > 5 and nq > 5.
The standard normal, since np < 5 and nq < 5.
The Student's t, since np < 5 and nq < 5.
The standard normal, since np > 5 and nq > 5.
Correct: Your answer is correct.
What is the value of the sample test statistic? (Round your answer to two decimal places.)

1.66

Correct: Your answer is correct.

(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

.0485

Incorrect: Your answer is incorrect.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Double the p-value you obtain here for a two-way test. It is true that the 95th percentile critical value test statistic is 1.645, but when you make it a two-way test at 95%, the 5% is divided up on both sides, and the critical value is at the 2.5 and the 97.5 percentiles. If you have an alpha of 0.01, then you look at the z0.995 value, which is 2.576. The p-value is 0.0969.
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