Problem 1: A statistician for a drug company wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines which are CNS stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).


Boys Cylert: 12, 10, 13, 10, 9, 12, 13, 10, 11, 12
Boys Placebo: 5, 6, 7, 6, 4, 5, 6, 7, 5, 7
Boys Ritalin: 3, 2, 5, 6, 1, 4, 2, 6, 1, 5
Girls Cylert: 5, 6, 2, 4, 3, 2, 4, 6, 2, 4
Girls Placebo: 4, 6, 7, 6, 5, 4, 5, 6, 7, 7
Girls Ritalin: 12, 9, 14, 13, 9, 12, 8, 15, 12, 11
  
1. The sum of squares for gender are

A child psychologist believes that controlled physical outbursts of anger (like punching a pillow) may improve the mood of young boys with emotional impairment. He believes that the proportion of boys that would benefit from this treatment is greater than the proportion of girls. A random sample from each population receives counseling in the treatment and is asked about their mood after an episode (x is the number of test subjects that reported an improvement in mood). The results of the study are summarized in the table below.

8) (3 points) Find the percentage of children that reported an improved mood from each group. Compare the percentages between boys and girls. Do the initial (untested) findings show what the psychologist expected?

9) (4 points) Assuming the conditions for a two proportion z-test hold, state the alternative hypothesis then find the observed test statistic and p-value. Round to the nearest hundredth.

10) (3 points) State your decision regarding the null hypothesis, H0: p1 = p2. How do the test results compare to the expectations of the psychologist?

In my grade 10 class there are there are 16 boys and 9 girls. I need to send 10 of them to a Guidance meeting. How many ways can...

a) an equal number of each gender be chosen?

b) Christopher be chosen?

c) Christopher and Emma be chosen?

d) at least one girl be chosen?

e) Christopher and Emma cannot both go, at least 1 of them must stay in class!

f) Send only girls?

Clearly label each part and show your calculations.

1.) A recent survey showed that high school girls average 110 text messages daily. The population standard deviation is 25 text messages. 1 In repeated samples of size n = 64 high school girls, the expected value of the sample mean is,

a 1.719 b 10.488 c 13.75 d 110

2.) In repeated samples of size n = 64 high school girls, the standard error of the sample mean is,

a 25 b 5 c 3.125 d 0.391

3.) In repeated samples of size n = 64 high school girls, the fraction of sample means that fall within ±5 messages from the population mean is,

a 0.8904 b 0.9260 c 0.9538 d 0.9824

4.) The margin of error for the middle interval which includes 95% of means from samples of size n = 64 is,

a 5.763 b 5.941 c 6.125 d 6.248

Consider the physical and psychosocial aspects of puberty. What is happening physiologically that is impacting behavior during puberty? What do you think is the hardest thing for young teens to adjust to during this transitional time? What are the possible causes and outcomes of early development in boys and girls?

According to a survey, high school girls average 100 text messages daily. Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken.

What is the probability that the sample is more than 105?
Please provide an answer with 3 decimal point.

About a decade ago, the incoming Republicans in the House of Representatives said they would institute a new practice. They could decide to do this because they were in the majority. The plan was that, before a new session began, Republican members would read the US Constitution aloud. (I’m sure that part of the motive was patriotism, but I think it’s also fair to say that their implicit suggestion was that many laws the previous Democratic majority had passed were unconstitutional. Certain unfortunate parts of the full Constitution were to be omitted, I think.)

The Democrats then asked to participate in the reading, and that’s what happened in the end -- various members of both parties stepped up to the podium and read each section of the Constitution.

Consider the following game. Its moves are made sequentially, and so it is easiest to represent it as a tree. There are two players - the group of House Republicans and the group of House Democrats. The Republicans decide whether to announce the practice of reading the Constitution or to not announce that. If they do not announce it, the game ends and the parties receive certain payoffs. Announcing it means that they’ll do it. If the Republicans do announce the new practice, the Democrats decide whether to request to join them in the reading, or to not request that. If the Democrats do not request that the game ends and the parties receive certain payoffs. If the Democrats do request that, then the Republicans decide whether to let the Democrats join the reading, or not to let them. In either case the game ends, with certain payoffs.

(a) Draw the tree, labeling the players and the moves. You can call the moves A, NA, for announce and not announce the plan, R an NR for request and not request to join, and L and NL for let or not let the Democrats join. Add reasonable payoffs.

(b) List the strategies for each party.

7. In class I talked about the children going to a birthday party and choosing one room or the other, room A or room B. They make the choice first, then have to spend the whole party in that room. There are 6 girls and 6 boys.

(a) each boy wants to be in a room with three girls and each girl wants to be in a room with three boys. Give an equilibrium

(b) Is it an equilibrium for all 12 to choose room A?

(c) how about each girl wants to be in a room with an even number of boys, and each boy wants to be in a room with an even number of girls.

Boys & Girls (a new e-dating service) undertakes two different online dating events that are popular items in the online-dating market: Hot (H) and Cool (C).  The profit margin on (Hot) H is $ 300; on C is $ 200.  For each couple that signs up with Hot (H), it takes the firm 6 hours of back-up checks (B), 4 hours of data entry (D), and 5 hours of interview (I). For each couple that signs up with Cool (C), it takes the 3 hours of B (back-up checks), 6 hours of D (data entry), and 5 hours of interview (I).  If 54 hours are available for B, 48 hours for D, and 50 hours for I, then how many slots of Hot (H) and Cool (C) should the company make available for potential customers.  Obviously, the company wants to maximize profits.              

Use this space to graph the constraints and derive the feasible set.  If you want you can scan the image and paste it here, or you can upload it in BB as another document.  Or the simplest is to copy and paste my figure from Unit 11 and relabel and change the entries on the axes.

URGENT!!!
Can you please solve this example in 50 minutes.

In the school, 70% of boys play basketball, 85% play soccer while 65% of boys play both sports.

a) Find the probability that the randomly chosen boy from the school plays at least one of those sports.

b) The director of the school organized a meeting with Miralem Pjanić and invited all the boys that play soccer. Miralem asked them how many of them play basketball too. What percentage of affirmative responses did he receive? (Enter the percentage to 2 decimal places.)

c) Are the events „The boy plays soccer“ and „The boy plays basketball“ independent? (Check the calculation and then enter 0 for "NO" or 1 for "YES".)