Question

In: Statistics and Probability

Although older Americans are most afraid of crime, it is young people who are more likely...

Although older Americans are most afraid of crime, it is young people who are more likely to be the actual victims of crime. It seems that older people are more cautious about the people with whom they associate. A national survey showed that 10% of all people ages 16-19 have been victims of crime.† At Jefferson High School, a random sample of

n = 68 students

(ages 16-19) showed that

r = 9

had been victims of a crime. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer.

(a) Do these data indicate that the population proportion of students in this school (ages 16-19) who have been victims of a crime is different (either way) from the national rate for this age group? Use

α = 0.05.

Do you think the conditions

np > 5

and

nq > 5

are satisfied in this setting? Why is this important?

(i) What is the level of significance?

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(b) Find a 95% confidence interval for the proportion of students in this school (ages 16-19) who have been victims of a crime.

lower limit    
upper limit    


(c) How large a sample size should be used to be 95% sure that the sample proportion is within a margin of error

E = 0.05

of the population proportion of all students in this school (ages 16-19) who have been victims of a crime? Hint: Use sample data as a preliminary estimate for p. (Round your answer up to the nearest student.)
students

Solutions

Expert Solution

(a)

(a) (i) What is the level of significance? 0.05

The null and alternate hypotheses:

H0: p = 0.10; H1: p ≠ 0.10

(ii) The standard normal, since np > 5 and nq > 5.

The test statistics is: z =0.89

(iii) The p-value is 0.3735

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

(v)There is insufficient evidence at the 0.05 level to conclude that there is a difference from the national average for the population proportion of crime victims.

(b)

(c)


Related Solutions

Although older Americans are most afraid of crime, it is young people who are more likely...
Although older Americans are most afraid of crime, it is young people who are more likely to be the actual victims of crime. It seems that older people are more cautious about the people with whom they associate. A national survey showed that 10% of all people ages 16-19 have been victims of crime.† At a high school, a random sample of n = 65 students (ages 16-19) showed that r = 11 had been victims of a crime. Note:...
Although older Americans are most afraid of crime, it is young people who are more likely...
Although older Americans are most afraid of crime, it is young people who are more likely to be the actual victims of crime. It seems that older people are more cautious about the people with whom they associate. A national survey showed that 10% of all people ages 16-19 have been victims of crime.† At a high school, a random sample of n = 66 students (ages 16-19) showed that r = 10 had been victims of a crime. Note:...
are persons with disabilities more likely to be victims of crime ?explain
are persons with disabilities more likely to be victims of crime ?explain
The USDA is concerned that most farmers are older Americans. In 2000, it was reported that...
The USDA is concerned that most farmers are older Americans. In 2000, it was reported that 25% of all US farmers were over the age of 65. In 2020, a random sample of 350 US farmers was taken and it was found that 98 were over the age of 65. The USDA claims that the proportion of all farmers who are over the age of 65 is now greater than 25%. Does this provide evidence to support the USDA’s claim...
Who are the people (groups, agencies,persons) most likely to benefit from the legalization of marijuana if...
Who are the people (groups, agencies,persons) most likely to benefit from the legalization of marijuana if It becomes policy? Do the advantages outweigh tbe disadvantages? Please respond in detail I want to learn as much as I can.
Explain the pitfalls in the following statements. a. People who play golf are more likely to own
Explain the pitfalls in the following statements.a. People who play golf are more likely to own a luxury car than people who do not play golf. Therefore, owning a luxury car causes people to play golf.b. Oscar Johansson noted that when he buys new shares of a company’s stock listed on Nasdaq Stockholm, the stock price usually increases if he takes a shower after making his decision. Last night, Oscar bought some shares of a company and went home to...
A reading group claims that Americans read more as they grow older. A random sample of...
A reading group claims that Americans read more as they grow older. A random sample of 45 Americans age 60 and older read for a mean length of 62.8 minutes per day, with a population standard deviation of 18.3 minutes per day. A random sample of 88 Americans between ages 50 and 59 read for a mean length of 53.9 minutes per day, with a population standard deviation of 23.1 minutes per day. At the 0.01 level of significance, test...
Are very young infants more likely to imitate actions that are modeled by a person or...
Are very young infants more likely to imitate actions that are modeled by a person or simulated by an object? This question was the basis of a research study. One action examined was mouth opening. This action was modeled repeatedly by either a person or a doll, and the number of times that the infant imitated the behavior was recorded. Twenty-seven infants participated, with 12 exposed to a human model and 15 exposed to the doll. Summary values are shown...
On the basis of adverse selection and moral hazard, who among the young, older persons, healthy...
On the basis of adverse selection and moral hazard, who among the young, older persons, healthy individuals and those who are ill, would be able to buy health insurance and seek medical services?
The most likely relationship between learning disorders and behavior problems in young children is that A....
The most likely relationship between learning disorders and behavior problems in young children is that A. behavior problems interfere with the learning environment and may lead to later learning disorders B. learning disorders are frustrating for children and may lead them to act out C. the two are distinct disorders that arise separately but increase the potency of either or both problems over time D. none of these
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT