How many ways are there to select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistinguishable Republicans, indistinguishable Independents if every party must have at least two members on the committee? If, in addition, no group have a majority of the committee members?

Suppose a long jumper claims that her jump distance is less than 16 feet, on average. Several of her teammates do not believe her, so the long jumper decides to do a hypothesis test, at a 10% significance level, to persuade them. she makes 19 jumpes. The mean distance of the sample jumps is 13.2 feet. the long jumper knows from experience that the standard deviation of her jump distance is 1.5 ft

A. State the null and alternate hypothesis

B. Compute the test statistic

C. State long jupers conclusion (you can use p value or Critical value)

Simulate a distribution of 500 t-scores with 24 degrees of freedom into a variable called tsim using the rt() function. Solve using R.

A student records the repair cost for 13 randomly selected TVs. A sample mean of $72.19 and standard deviation of $15.88 are subsequently computed. Determine the 98% confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal.

1) Find the critical value that should be used in constructing the confidence interval. Round you answer to three decimal places.

2) Construct the 98% confidence interval. Round your answer to two decimal places.

The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is equipped with three doors. Behind two are goats, and behind the third is a car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, someone who knows wh at's behind the doors (Monty Hall) opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door which neither you picked nor he opened). The Monty Hall problem is deciding whether you change your selection or not that has a better chance of winning the car . It’s common sense that if not to change, the probability of winning is 1/3 but what about changing the selection.

Simulating this game using SAS, for each round, program the fol lowing, 1) Assigning two goats and a car to three doors randomly 2) Picking a door randomly 3) Picking one of the two remaining doors to open but must showing the goat 4) Changing the selection to the remaining door 5) Deciding the result Repeating these steps for 100 round s , generating a data set including the following five variables, the round number, the door the car is in, the door chosen initially, the door chosen after switching, and the result(win/lose). Showing the data set and r eporting the frequenc y of the i nitial door chosen, the frequenc y of the door chosen at the end, the average rate of winning.

In a recent study, among recently-graduated university students of the sample, only 4% of them wrote with their left hand. Yet, among grade 1 elementary-school students from the same sample, a full 20% of them wrote with their left hand. What is wrong with the conclusion from these data that writing with the left hand is bad for university success?

In the early 1900s, Latter (1902) investigated the behavior of female cuckoos, that lay their eggs on the ground and then move them to the nests of other birds. In particular, Latter gathered data on the lengths of the cuckoo eggs found in these foster-nests. Data based on this work is used in (Tippett, 1952) and is located in the file cuckoos. The data contains the lengths, in millimeters, of the lengths of cuckoo eggs and the species of the nests where the eggs were placed. Get the data by installing and loading the resampledata R package, and use the Cuckoos dataset.

a. Create side-by-side boxplots (in R) to compare the distribution of lengths across the different foster nests.

b. Conduct an ANOVA test (also in R) to see if the mean lengths of the cuckoo eggs are the same across the different foster nests.

c. Perform the Tukey Honestly Significant Difference test (without p-value adjustment) to compare all pairwise means. What can you conclude from this analysis? d. Do the Tukey HSD test using the p-value adjustment method of your choice. Do your conclusions from “2c” change? Given the number of pairwise contrasts, without p-value adjustment, what would be your family-wise error rate if you were to conduct each pairwise contrast at /alpha = .05?

Using R, conduct an ANOVA to see if there are differences in weight between two groups of monkeys. What is null hypothesis conclusion with evidence.

Conduct a post-hoc MCP (use TukeyHSD) to see which means are different. What do the outputs lwr and upr mean?

The numbers are

monkey group 1= 9.7, 9.2, 9.5, 9.5, 10.9, 9.8, 8.7, 7.9, 9.8, 9, 10.5, 8.9, 10, 8.9, 6.8, 9.3, 8.2, 8.5, 9.4, 10.5

Monkey group 2= 8.1, 7.8, 7.6, 9.9, 8.1, 9.1, 8.8, 10.4, 8.6, 6.9, 9.1, 6.7, 7.3, 7.8, 9.6, 8.7, 5.5, 9.5, 8.2, 7.8

Please Conduct a Paired Difference Test (use α=5%) for the two data sets below. Thanks.

2012          2015

Seventy percent of adults favor some kind of government control on the prices of medicines. A random sample of 400 adults was selected to determine whether or not they favor some kind of government control.

(a) Are the conditions necessary to apply the CLT satisfied? Explain.

(b)Describe and sketch the sampling distribution of the sample proportion in this situation.

(c) Find the probability that the proportion of adults who favor some kind of government control is less than 0.65.

(d)Find the probability that the proportion is between 0.73 and 0.76.

A food company has developed a high mineral sea salt (sodium). A nurse practitioner wants to know if blood pressure can be predicted from the sodium intake of the new sea salt. Below are the sodium and BP measurements for a sample of participants that regularly use the new sea salt. What can the nurse practitioner conclude with α = 0.01?

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected a):

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
Critical value =  ; Test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

More sodium intake significantly predicts an increase in blood pressure.More sodium intake significantly predicts a decrease in blood pressure.    Sodium intake does not significantly predict blood pressure.

A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21. I just need G.

a.)If you take a sample of size 10, can you say what the shape of the distribution for the sample mean is? Why?

b.) For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean.

c.) For a sample of size 10, find the probability that the sample mean is more than 241.

d.) If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? Why?

e.) For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.

f.) For a sample of size 35, find the probability that the sample mean is more than 241.

g.) Compare your answers in part c and f. Why is one smaller than the other?

Pre-Employment Drug Screening Results are shown in the following Table:

If 1 of the 200 test subjects is randomly selected, find the probability that the subject had a positive test result, given that the subject actually uses drugs. That is,

(positive test result subject uses drugs).

If 1 of the 200 test subjects is randomly selected, find the probability that the subject actually uses drugs, given that he or she had a positive test result. That is,

(subject uses drugs ).

The mean per capita income is 15,654 dollars per annum with a standard deviation of 570

dollars per annum.

What is the probability that the sample mean would differ from the true mean by less than  63 dollars if a sample of 315 persons is randomly selected? Round your answer to four decimal places.

The presence of student-owned information and communication technologies (smartphones, laptops, tablets, etc.) in today's college classroom creates learning problems when students distract themselves during lectures by texting and using social media. Research on multitasking presents clear evidence that human information processing is insufficient for attending to multiple stimuli and for performing simultaneous tasks.

To collect data on how multitasking with these technologies interferes with the learning process, a carefully-designed study was conducted at a mostly residential large public university in the Northeast United States. Junco, R. In-class multitasking and academic performance. Computers in Human Behavior (2012)

At the beginning of a semester a group of students who were US residents admitted through the regular admissions process and who were taking the same courses were selected based on their high use of social media and the similarities of their college GPA's. The selected students were randomly assigned to one of 2 groups:

group 1 students were told to text and use Facebook during classes in their usual high-frequency manner;

group 2 students were told to refrain from any use of texting and Facebook during classes.

At the conclusion of the semester the semester GPA's of the students were collected. The results are shown in the table below.

IN-CLASS MUTLITASKING STUDY

Frequent Facebook Use and Texting   

x₁ = 2.87

s₁ = 0.67

n₁ = 65

No Facebook Use or Texting

x₂ = 3.16

s₂ = 0.53

n₂ = 65

Do texting and Facebook use during class have a negative affect on GPA? To answer this question perform a hypothesis test with
H₀: μ₁−μ₂ = 0
where μ₁ is the mean semester GPA of all students who text and use Facebook frequently during class and μ₂ is the mean semester GPA of all students who do not text or use Facebook during class.

Question 1. What is the value of the test statistic for this hypothesis test?

Question 2. What is the P-value for this hypothesis test?