In: Statistics and Probability

A recent study of high school students shows the percentage of females and males who have at LEAST one notation in their school record for inappropriate behavior. A simple random sample of high school students was interviewed. The students were asked whether they had a notation for inappropriate behavior in their school record. Of the 100 females, 21 answered yes, as did 145 of the 400 males.

Part A: Construct and interpret a 99% confidence interval for the difference in population proportions of females and males who have at LEAST one notation for inappropriate behavior. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points) (10 points)

In a recent survey of county high school students, 100 males and
100 females, 66 of the male students and 47 of the female students
sampled admitted that they consumed alcohol on a regular basis.
Find a 90% confidence interval for the difference between the
proportion of male and female students that consume alcohol on a
regular basis. Can you draw any conclusions from the confidence
interval?
For the test of significance questions, clearly indicate each of
the formal steps...

In a certain high school, uniforms are optional. A study shows
that high school students who wear uniforms have a lower grade
average than students who don't wear uniforms. From this study, the
school administration claims that they should not require the
students to wear uniforms because that is the cause of the lowering
grades. Another possible explanation is that students who wear
uniforms are poorer than the students who don't wear uniforms and
the economic situation of their parents...

A recent study shows that unemployment does not impact males and
females in the same way (Newsweek, April 20, 2009).
According to a Bureau of Labor Statistics report, 8.5% of those who
are eligible to work are unemployed. The unemployment rate is 8.8%
for eligible men and only 7.0% for eligible women. Suppose 52% of
the eligible workforce in the U.S. consists of men.
a. You have just heard that another worker in a
large firm has been laid off....

A study wants to compare the
percentage of Facebook users between males and females in a county.
A sample of 95 males shows that 46 of them use Facebook. A sample
of 90 females shows that 48 of them use Facebook.
(a) What are the populations?
(b) At α = 0.01 level of significance, is there evidence that
the two population proportions are different?
(c) Identify the type of error for your conclusion. If it is
type I error, find...

We are interested in comparing the percentage of females versus
males who feel they are overweight. The following data was
collected:
What is the 95% confidence interval for the difference in
proportion between women and men?
What is the test statistic?
Male or Female
Total Surveyed
Number who feel they are overweight
Female
146
32
Male
84
15

After the recent school shooting in Florida, high school
students have led the protests demanding stricter gun laws. After
the Treyvon Martin shooting five years ago, young people started
the Black Lives Matter movement. Based on emotional and social
development in adolescence, why do you think these young people
were the ones to work for change?

In a recent school year in the state of Washington, there were
319,000 high school students. Of these, 154,000 were girls and
165,000 were boys. Among the girls, 41,100 dropped out of school,
and among the boys, 10,500 dropped out. A student is chosen at
random. Round the answers to four decimal places.
(a) What is the probability that the student is female?
(b) What is the probability that the student dropped out?
(c) What is the probability that the...

In a recent survey of high school students, it was found that
the amount of time spent on reading books per week was normally
distributed with a mean of 32 minutes. Assume the distribution of
weekly reading time follows the normal distribution with a
population standard deviation of 2 minutes. Suppose we select a
sample of 20 high school students.
a. What is the standard error of the mean time?
Answer
b. What percent of the sample means will be...

A recent study found that toddlers who have a diet high in
processed foods may have a slightly lower IQ later in life. The
conclusion came from a long-term investigation of 14,000 people
whose health was monitored at 3,4,7, and 8 years of age.
e) One analysis found that of the 4000 children for which there
were complete data, there was a significant difference in IQ
between those who had had “processed” (i.e., junk) food and those
who followed health-conscious...

A recent Pew Center Research survey revealed that 68% of high
school students have used tobacco related products. Suppose a
statistician randomly selected 20 high school students. Use this
information to answer questions 39-41.
To find the probability that exactly 15 used tobacco products,
would you use the Binomial, Geometric, or Poisson distribution to
find the probability?
Set up the problem to find P (X = 15) using the appropriate
distribution. Do NOT solve.
What is the expected number of...

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