Question 1

A recent national survey found that high school students watched an average of 6.8 videos per month. A random sample of 36 high school students revealed that the mean number of vidoes watched last month was 6.2. From past experience it is known that the population standard deviation of the number of vidoes watched by high school students is 0.5. At the 0.05 level of signifiance, can we conclude that high school students are watching fewer vidoes?

(a) State the null and alternative hypotheses for this test.

(b) Compute the value of the Test Statistic?

(c) State the p-value for this test.

(d) State the conclusion for the test. Give reasons for your answer.

Question 2

From past records it is known that the average life of a battery used in a digital clock is 305 days. The lives of the batteries are normally distributed. The battery was recently modified to last longer. A sample of 40 modifed batteries was tested. It was discovered that the mean life was 311 days, and the sample standard deviation was 22 days. At the 0.01 level of sigificance, did the modofication increase the mean life of the battery?

(a) State the null and alternative hypotheses for this test.

(b) Compute the value of the Test Statistic?

(c) State the critical region for this test.

(d) State the conclusion for the test. Give reasons for your answer.

Question 3

A machine is set to produce no more than 0.07 defectives when properly adjusted. After the machine had been in operation for some time, a sample of one hundred pieces was tested. Twenty defectives pieces were observed. Is there evidence at the 5% level of significance that the machine needs readjustment?

(a) State the null and alternative hypotheses for this test.

(b) Compute the value of the Test Statistic?

(c) State the p-value for this test.

(d) State the conclusion for the test. Give reasons for your answer.

2. Identify the type of sampling used: self-response, random, systematic, convenience,

stratified, or cluster.

a. DTE survey 20 households in every city in

the County to learn about the costumer

satisfying level.

b. A sample consists of students with even

number Student’s ID.

c. A market researcher selects 100 people

from each state in the USA.

d. A pollster uses a computer to generate 500

random numbers, then interviews the voters

corresponding to those numbers.

e. To check the alcohol level of drivers,

police officers stopped every seventh car

passing through a side street near a

famous bar.

f. A University committee wants to know the

percentage of students who drive and text.

They survey all students majoring in History

and English.

g. A restaurant decided to give free

dessert for every 50th costumer dining

there.

h. A reporter writes the name of each US

senator on a separate card, shuffles the

cards, and then draws five names.

i. There are 4 bags of M&M in a box. One

consists of blue M&M, another bag has

red only M&M, the other two consists of

chocolate and yellow M&M respectively.

Lisa takes out 5 M&M from each bag to

create a sample of M&M.

j. A researcher conducts a survey by asking

100 randomly selected workers from each

category: no high school degree, high school

degree, more than high school degree.

k. A researcher wants to determine the

percentage of first grader still believe in

Santa Claus. He uses the first graders in

his son’s school as his sample.

l. A polling on Twitter asks its follower to rank

the work ethic of the congress from 1 to 5,

with 1 as the lowest and 5 as the highest

1.       A   university   researcher   is   interested   in   whether   recent   recruitment   efforts   have   changed   the   type   of   students   admitted   to   the   university.   To   test   this,   she   randomly   selects   50   freshmen   from   the   university   and   records   their   high   school   GPA.   The   mean   is   2.90   with   a   standard   deviation   of   0.70.   The   researcher   also   knows   that   the   mean   high   school   GPA   of   all   freshmen   enrolled   at   the   university   five   years   ago   was   2.75   with   a   standard   deviation   of   0.36.   The   researcher   wants   to   know   if   the   high   school   GPA   of   current   freshmen   at   the   university   is   different   than   that   of   freshmen   from   five   years   ago.  
   (a)   What   are   the   null   and   alternative   hypotheses   in   this   study   (stated   mathematically)?  
   (b)   Should   the   researcher   use   a   one-tailed   or   a   two-tailed   test?  
   (c)   Compute   the   appropriate   test   statistic   for   testing   the   hypothesis.  
   (d)   Using   α   =   0.05,   what   do   you   conclude   about   the   high   school   GPA   of   current   freshman?   Be   sure   to   include   a   discussion   of   the   critical   value   in   your   answer.  
   (e)   What   type   of   error   might   the   researcher   be   making   in   part   (d)?  
  
   2.   A   researcher   believes   that   smoking   worsens   a   person’s   sense   of   smell.   To   test   this,   he   takes   a   sample   of   25   smokers   and   gives   them   a   test   of   olfactory   sensitivity.   In   this   test,   higher   scores   indicate   greater   sensitivity.   For   his   sample,   the   mean   score   on   the   test   is   15.1   with   a   standard   deviation   of   1.2.   The   researcher   knows   the   mean   score   in   the   population   is   15.5,   but   the   population   standard   deviation   is   unknown.  
   (a)   What   are   the   null   and   alternative   hypotheses   in   this   study   (stated   mathematically)?  
   (b)   Should   the   researcher   use   a   one-tailed   or   a   two-tailed   test?  
   (c)   Compute   the   appropriate   test   statistic   for   testing   the   hypothesis.  
   (d)   Using   α   =   0.01,   do   you   conclude   that   smoking   affects   a   person’s   sense   of   smell?   Be   sure   to   include   a   discussion   of   the   critical   value   in   your   answer.  
   (e)   What   type   of   error   might   the   researcher   be   making   in   part   (d)?  
  

Christy was referred to the school social worker due to high absenteeism. When the social worker made a home visit, Christy’s mother stated that her daughter’s absences resulted from Christy’s frequent complaints of feeling sick to her stomach. The mother disclosed that Christy had been involved in a bicycle accident more than two years ago, resulting in a separation of her cartilage from the ribcage when her chest hit the handle bars. Due to this painful condition, Christy missed more than a month of school and subsequently had to repeat the third grade.

Christy’s mother enrolled her in a private school for that year. Christy re-enrolled at her home school this year; however, her friends are all in the next grade level. Since the accident, Christy often complains of not feeling well. She is very thin, and her teacher has noticed that her lunch is often left on her plate, barely touched. At home, Christy is often irritable and moody. She doesn’t seem to have much interest in doing anything. The family is under considerable financial strain and lived with extended family until recently. Christy has had to share a bedroom with her younger sister, who is in the same grade as Christy. They do not get along.

Last week, after a brutal argument with her sister, Christy ran out of the house crying and saying she was going to kill herself. Her mother wondered if she was doing this just to get attention, because she did not believe that someone as young as Christy could actually be depressed.She was hoping Christy would just get over it.

in 100 words

Discuss one assessment that you might use to evaluate the level and severity of symptoms that Christy presents.

Please use references and citations

Christy was referred to the school social worker due to high absenteeism. When the social worker made a home visit, Christy’s mother stated that her daughter’s absences resulted from Christy’s frequent complaints of feeling sick to her stomach. The mother disclosed that Christy had been involved in a bicycle accident more than two years ago, resulting in a separation of her cartilage from the ribcage when her chest hit the handle bars. Due to this painful condition, Christy missed more than a month of school and subsequently had to repeat the third grade.

Christy’s mother enrolled her in a private school for that year. Christy re-enrolled at her home school this year; however, her friends are all in the next grade level. Since the accident, Christy often complains of not feeling well. She is very thin, and her teacher has noticed that her lunch is often left on her plate, barely touched. At home, Christy is often irritable and moody. She doesn’t seem to have much interest in doing anything. The family is under considerable financial strain and lived with extended family until recently. Christy has had to share a bedroom with her younger sister, who is in the same grade as Christy. They do not get along.

Last week, after a brutal argument with her sister, Christy ran out of the house crying and saying she was going to kill herself. Her mother wondered if she was doing this just to get attention, because she did not believe that someone as young as Christy could actually be depressed.She was hoping Christy would just get over it.

in 100 words

What are the risk and protective factors identified? Rate the level of symptoms that Christy presents for suicide or self-harm.

Please use references and citations

The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a sample of n=30 books and records the publication date for each. The sample produces an average age of M=23.8 years with a variance of s2 =67.5. Use this sample to conduct a one-tailed test with α=.01 to determine whether the average age of the library books in significantly greater than 20 years. Compute r2 and interpret..

Hypothesis Testing (Complete the four steps below)

STEP 1: State the hypotheses and set the alpha level (3 points)

STEP 2: Locate the critical region (3 points)

STEP 3: Compute the test statistic for the sample (6 points)

STEP 4: Make a decision and state your conclusion about H0 based on the result of step 3 (4 points) Compute and interpret r2. (4 points)

The registrar of a law school has compiled the following statistics on the progress of the school's students working toward the LLB degree: Of the first-year students in a particular year, 80% successfully complete their course of studies and move on to the second year, whereas 20% drop out of the program; of the second-year students in a particular year, 92% go on to the third year, whereas 8% drop out of the program; of the third-year students in a particular year, 98% go on to graduate at the end of the year, whereas 2% drop out of the program.

(a) Construct the transition matrix associated with the Markov process. (Label your matrix using this order: Drop out, Graduate, First-Year, Second-Year, Third-Year)

(b) Find the steady-state matrix. (Round your answers to four decimal places.)

(c) Determine the probability that a beginning law student enrolled in the program will go on to graduate. (Round your answer to four decimal places.)

In an experiment to determine the effect of nutrition on the attention spans of elementary school students, a group of 45 students is divided into three groups of 15, and randomly assigned to each of three meal plans: no breakfast, light breakfast, and full breakfast. Their attention spans, in minutes, were recorded. Say you want to test the hypothesis that the means of the attention spans are not all the same at a level of significance of 5%.

(a) (3 pts) What are the null and alternative hypotheses?

(b) (4 pts) Suppose that you find MSG=26 and MSE=3.1. Find the F-statistic, and estimate the p-value of your data using the F-table.

(c) (3 pts) Should you accept or reject? Explain.