A nationwide award for high school students is given to outstanding students who are sophomores, juniors, or seniors (freshmen are not eligible). Of the award-winners, 65 percent are SENIORS, 20 percent JUNIORS, and 15 percent are SOPHOMORES.

Note: Your answers should be expressed as decimals rounded to three decimal places.

(a) Suppose we select award-winners one at a time and continue selecting until a SENIOR is selected. What is the probability that we will select exactly three award-winners?

(b) Suppose we select award-winners one at a time and continue selecting until a JUNIOR is selected. What is the probability that we will select at least three award-winners?

(c) Suppose we select award-winners one at a time continue selecting until a SOPHOMORE is selected. What is the probability that we will select 2 or fewer award-winners?

Albany High School is planning a field trip for senior students. They expected 100 students to participate in the trip but eventually 130 students join the trip. They planned to charge each student a price of $25 for the trip and spend an expense of $20 per student for the trip. Then, they find that the expense of the filed trip goes up to $30 per student, and they have to increase the price for each student to $40.

Budget Actual

Number of students 100 130

Revenue per student $25 $40

Expense per student $20 $30

(1) What is the expense variance? Is it favorable or unfavorable? How would this variance affect the balance of the budget (aka: the profit)? (Hint: Homework 6 templates might be useful for this question, but you don’t need to follow the templates. No need to consider Quantity (input) in this question.)

(2) What is the revenue variance? Is it favorable or unfavorable? How would this variance affect the balance of the budget (aka: the profit)? (Hint: Homework 6 templates might be useful for this question, but you don’t need to follow the templates. No need to consider the Mix in this question.)

(3) What is the total variance (revenue variance and expense variance together)? Is it favorable or unfavorable? How would this variance affect the balance of the budget (aka: the profit)?

Students arrive at a local bar at a mean rate of 30 students per hour. Assume that the bouncer waits X (minutes) to card the next student. That is, X is the time between two students arriving at the bar. Then we know that X has approximately an exponential distribution. What is the probability that nobody shows up within the 2 minutes after the previous customer? What is the probability that the next student arrives in the third minute, knowing that nobody has shown up in the 2 minutes since the previous student?

College students Suppose a recent study of 1,000 college students in the U.S. found that 8% of them do not use Facebook. Which of the following describes the population for this example?

-All College students in the US

-The 1000 college students who participated in the study

-all college students in the US who do not use facebook

-The 8% of college students who do not use facebook

Which of the following defines what is meant by a control group in an experiment

-A group that is handled identically to the treatment groups in all respects except that they are controlled to greater extend than the other groups, providing baseline data.

-a group that is used by researchers to monitor how the experiment is going

-a group that is handled identically to the treatment group in all respects except that they dont recieve the active treatment

-none of the above

Which of the following studies can result in researchers extending the results inappropriately because the sample doesn’t represent the intended population?

-Studies involving randomly selected participants

-studies involving convenience samples

-experimental studies

-all of the above

Without random assignment, which of the following can happen?

-naturally occuring confounding variables can result in an apparent relationship between the explanatory and response variables

-the results may not be able to extend to a larger population

-Many people in the study will drop out because they aren’t happy with the treatment they were assigned to. This will cause bias in the results

-none of the above

Making a Type I error is only possible if the ____ hypothesis is true.

-alternative

-null

-power

-none of above

The National Collegiate Athletic Association (NCAA) requires colleges to report the graduation rates of their athletes. Here are data from a Big Ten university's report: 45 of the 74 athletes admitted in a speci fic year graduated within 6 years. Does the proportion of athletes who graduate di ffer significantly from the all-university proportion, which is .70 ?

What is the sample size

-45

-74

-119

-0.029

What is the sample proportion?

-6

-0.61

-6

-65

What are the null and alternative hypotheses?

-Null: p>0.70; alternative: p <0.61

-Null: p=.61; alternative: p <.0..61

-Null: p=0.70; alternative: p is not 0.70

-Null: p=.70; alternative: p > .70

What is the value of the test statistic for your observed results?

-1.70

- (-)2.70

- (-) 1.70

-0.53

What is the p-value for your observed results?

-0.9554

-0.0892

-0.002

-0.998

What is your conclusion? Please use words that a non-statistics student would understand, and justify your answer. Assume a significance level of .05.

-Since the p-value (.9554) > .05, do not reject the null hypothesis. This means that the sample evidence is not strong enough to conclude that the proportion of athletes who graduate di ffer signi ficantly from the all-university proportion of 0.70

-Since the p-value (.0892) > .05, we failed to reject the null hypothesis. This means that the sample evidence is not strong enough to conclude that the proportion of athletes who graduate di ffer signi ficantly from the all-university proportion of 0.70

-Since the p-value (.998) > .05, reject the null hypothesis. This means that the sample evidence is not strong enough to conclude that the proportion of athletes who graduate di ffer signi ficantly from the all-university proportion of 0.70

-since the p-value (.002) < .05, reject the null hypothesis. This means that the sample evidence is strong enough to conclude that a larger proportion of peopleown bread machine than 3 years ago.

Based on your conclusion, what type of error are you risk at?

-type I error

-type II error

-type I and type II error

-none of the above

If the power of the test is 87% for this test, what is the probability of the test making type II error?

-larger than 87%

-13%

-87%

-not enough information

What is the 95% of confidence interval of proportion of athletes graduate within 6 years ?

-(0.302,0.398)

-(1.10.1.32)

-(0.496, 0.724)

Base on your result of 95% confidence interval, can you conclude that majority of the athletes graduate within 6 years?

-No, because 0.50 is in the interval.

-No, because 0.70 is in the interval

-Yes, because 0.40 is not in the interval.

1. A university found that 10% of students withdraw from a math course. Assume 25 students are enrolled.
   1. Write the prob. distribution function with the specific parameters for this problem

1. 2. Compute by hand (can use calculator but show some work) the pro that exactly 2 withdraw.
2. 3. Compute by hand (can use calculator but show some work) the prob. that exactly 5 withdraw.
3. 4. Construct the probability distribution table of class withdrawals in Excel. This is a table of x and f(x). Generate one column for the number of x successes with numbers 0 to 25 in each row. Generate a second column with the probability f(x) of each success using the Excel function =BINOM.DIST(x, n, p, FALSE) in each row. Attach the table
4. 5. What is the probability that 5 or less will withdraw?

A nationwide award for high school students is given to outstanding students who are sophomores, juniors, or seniors (freshmen are not eligible). Of the award-winners, 60 percent are SENIORS, 24 percent JUNIORS, and 16 percent are SOPHOMORES.

Note: Your answers should be expressed as decimals rounded to three decimal places.

(a) Suppose we select award-winners one at a time and continue selecting until a SENIOR is selected. What is the probability that we will select exactly three award-winners?

(b) Suppose we select award-winners one at a time and continue selecting until a JUNIOR is selected. What is the probability that we will select at least three award-winners?

(c) Suppose we select award-winners one at a time continue selecting until a SOPHOMORE is selected. What is the probability that we will select 2 or fewer award-winners?

A measurement is normally distributed with μ=55μ=55 and σ=18σ=18. Round answers below to three decimal places.

(a) The mean of the sampling distribution of x¯x¯ for samples of size 36 is:

(b) The standard deviation of the sampling distribution of x¯x¯ for samples of size 36 is:

The state of California conducted an experiment with college students. Teachers and students were randomly assigned to be in a regular sized class or a small sized class. The dependent variable is the student’s score on a math test (MATHSCORE). Let SMALL = 1 if the student is in a small class and SMALL = 0 otherwise. The other variable of interest is the number of years of teacher experience, given by TCHEXPER. Let BOY = 1 if the stu- dent is male and BOY = 0 if the student is female.

a) (5 points) Write down the model for the dependent variable MATHSCORE as a function of SMALL, TCHEXPER, BOY and BOY*TCHEXPER, with pa-

rameters β1 , β2 , β2 , ... etc.

b) (5 points) What is the expected math score for a male student in a small class with a teacher having 10 years of experience? (Your answer will be in terms of the model parameters, including βi’s).

c) (5 points) What is the change in the expected math score for a male student

in a small class with a teacher having 11 years of experience rather than 10? d) (5 points) State the marginal effect of teacher experience on expected math scores.
e) (5 points) State, in terms of model parameters, the null hypothesis that the marginal effect of teacher experience on expected math score does not
differ between men and women, against the alternative that men benefit
more from teacher experience.

1. The mean age of College students is 25. A certain class of 33 students has a mean age of 22.64 years. Assuming a population standard deviation of 2.87 years, at the 5% significance level, do the data provide sufficient evidence to conclude that the mean age of students in this class is less than the College mean?

a. Set up the hypotheses for the one-mean ?-test. ?0:    ??:

b. Compute the test statistic. Round to two decimal places.

c. Sketch a normal curve, mark your value from part (b), and shade in the area(s) we are interested in. Determine the ?-value.

d. Determine if the null hypothesis should be rejected.

e. Interpret your result in the context of the problem in a sentence.

A study examined the effects of an intervention program to improve the conditions of urban bus drivers. Among other variables, the researchers monitored diastolic blood pressure of bus drivers in a large city. The data, in millimeters of mercury (mm Hg), are based on the blood pressures obtained prior to intervention for the 41 bus drivers in the study. At the 10% significance level, do the data provide sufficient evidence to conclude that the mean diastolic blood pressure of bus drivers in the city exceeds the normal diastolic blood pressure of 80 mm Hg? The mean of the data is ? = 81.95122 mm Hg, and the standard deviation of the data is ? = 10.537911 mm Hg.

a. Set up the hypotheses for the one-mean ?-test. ?0:   ??:   

b. Compute the test statistic. Round to two decimal places.

c. Sketch a ?-curve, mark your value from (b), and shade in the area(s) we are interested in. Determine the ?- value.

d. Determine if the null hypothesis should be rejected.

e. Interpret your result in the context of the problem in a sentence.

1/Suppose that about 84% of graduating students attend their graduation. A group of 37 students is randomly chosen, and let X be the number of students who attended their graduation.

Please show the following answers to 4 decimal places.

1. What is the distribution of X? X ~ ? B U N  (,)
2. What is the probability that exactly 29 number of students who attended their graduation in this study?
3. What is the probability that at least 29 number of students who attended their graduation in this study?
4. What is the probability that more than 29 number of students who attended their graduation in this study?
5. What is the probability that between 26 and 31 (including 26 and 31) number of students who attended their graduation in this study?

2/A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.13.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 23-year period

3/A local bakary has determined a probability distribution for the number of cheesecakes that they sell in a given day.

What is the probability of selling 15 cheesecakes in a given day?
What is the probability of selling at least 10 cheesecakes?
What is the probability of selling 5 or 15 chassescakes?
What is the peobaility of selling 25 cheesecakes?
Give the expected number of cheesecakes sold in a day using the discrete probability distribution?
What is the probability of selling at most 10 cheesecakes?

4/Find the mean of the following probability distribution? Round your answer to four decimal places.

μμ =

5/

A researcher gathered data on hours of video games played by school-aged children and young adults. She collected the following data.

Find the range.
( ) hours
Find the standard deviation. Round your answer to the nearest tenth, if necessary.
( ) hours
Find the five-number summary.

.

3) In a study of student loan subsidies, I surveyed 100 students. In this sample, students will owe a mean of $25,000 at the time of graduation with a standard deviation of $2,000.

(a) Develop a 96% confidence interval for the population mean.

(b) Develop a 96% confidence interval for the population standard deviation.