Question

Part 1) Education influences attitude and lifestyle. Differences
in education are a big factor in the "generation gap." Is the
younger generation really better educated? Large surveys of people
age 65 and older were taken in *n*_{1} = 36 U.S.
cities. The sample mean for these cities showed that
*x*_{1} = 15.2% of the older adults had attended
college. Large surveys of young adults (age 25 - 34) were taken in
*n*_{2} = 35 U.S. cities. The sample mean for these
cities showed that *x*_{2} = 19.2% of the young
adults had attended college. From previous studies, it is known
that *?*_{1} = 6.6% and *?*_{2} =
5.6%. Does this information indicate that the population mean
percentage of young adults who attended college is higher? Use
*?* = 0.01.

a) What is the value of the sample test statistic? (Test the
difference *?*_{1} ? *?*_{2}. Round
your answer to two decimal places.)

(b) Find (or estimate) the *P*-value. (Round your answer to
four decimal places.)

Part 2) 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, 23 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%.

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

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

(c) Based on your answers in parts (a) to (c), will you reject
or fail to reject the null hypothesis? Are the data statistically
significant at level *?*?

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

(d) Interpret your conclusion in the context of the
application.

There is sufficient evidence at the 0.05 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.

There is insufficient evidence at the 0.05 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.

Answer #1

1

a)

H0: The population mean percentage of people age 65 and older who
attended college is equal to that of young adults.

H1: The population mean percentage of people age 65 and older who
attended college is less than that of young adults.

As, we know the population standard deviations, ?1 and ?2 , we can use z test statistic to test the hypothesis.

Standard error of the mean difference, se =

Sample test statistic, z = (x1 - x2) / se

= (15.2 - 19.2) / 1.451206

= -2.7563

(b)

For one tail test,

P-value = P[z < -2.7563] = 0.0029

As, p-value is less than the significance levele of 0.01, we reject the null hypothesis H0 and conclude that there is significant evidence that population mean percentage of people age 65 and older who attended college is less than that of young adults.

Part 1) Education influences attitude and lifestyle. Differences
in education are a big factor in the "generation gap." Is the
younger generation really better educated? Large surveys of people
age 65 and older were taken in n1 = 40 U.S.
cities. The sample mean for these cities showed that
x1 = 15.2% of the older adults had attended
college. Large surveys of young adults (age 25 - 34) were taken in
n2 = 37 U.S. cities. The sample mean for...

Education influences attitude and lifestyle. Differences in
education are a big factor in the "generation gap." Is the younger
generation really better educated? Large surveys of people age 65
and older were taken in n1 = 37 U.S. cities. The sample mean for
these cities showed that x1 = 15.2% of the older adults had
attended college. Large surveys of young adults (age 25 - 34) were
taken in n2 = 38 U.S. cities. The sample mean for these cities...

14) 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...

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...

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...

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...

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...

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