What makes a dependent samples t test different from a one-sample t test? In what way are these tests similar?

Assume that you have a sample of n 1 equals 8​, with the sample mean Upper X overbar 1 equals 42​, and a sample standard deviation of Upper S 1 equals 4​, and you have an independent sample of n 2 equals 15 from another population with a sample mean of Upper X overbar 2 equals 34 and a sample standard deviation of Upper S 2 equals 5. What assumptions about the two populations are necessary in order to perform the​ pooled-variance t test for the hypothesis Upper H 0 : mu 1 equals mu 2 against the alternative Upper H 1 : mu 1 greater than mu 2 and make a statistical​ decision?

A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents have boycotted goods for ethical reasons.

1. In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?
2. In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?
3. In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons?
4. In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? Also find the standard deviation.

27. English editions of Scrabble have 100 letter tiles, distributed as follows and as above:

• 2 blank tiles (scoring 0 points)

• 1 point: E ×12, A ×9, I ×9, O ×8, N ×6, R ×6, T ×6, L ×4, S ×4, U ×4

• 2 points: D ×4, G ×3

• 3 points: B ×2, C ×2, M ×2, P ×2

• 4 points: F ×2, H ×2, V ×2, W ×2, Y ×2

• 5 points: K ×1

• 8 points: J ×1, X ×1

• 10 points: Q ×1, Z ×1

a. What is the mean point value of the full set of Scrabble tiles?

b. What is the median point value of the full set of Scrabble tiles?

Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 35 minutes and a standard deviation of 4 minutes, while Method B has a mean of 39 minutes and a standard deviation of 20 minutes.

(a) Which procedure is preferred if the procedure must be completed within 35 minutes? Method A, Method B, or Either?

(b) Which procedure is preferred if the procedure must be completed within 45.0 minutes? Method A, Method B, or Either?

(c) Which procedure is preferred if the procedure must be completed within 43 minutes? Method A, Method B, or Either?

PLEASE SHOW ANSWER WITHOUT USING EXCEL OR ANY SOFTWARE. NEED DETAILED WORKINGS OF THE ANSWER. PLEASE NOTE NO EXCEL

Conduct a test of hypothesis to determine whether the block of the treatment means differ. Using the .05 significance level:

1. State the null and alternate hypothesis for treatments
2. State the decision rule for treatments
3. State the null and alternate hypothesis for blocks
4. State the decision rule for blocks
5. Compute SST, SSB SS total, and SSE
6. Complete an ANOVA table
7. Give your decision regarding the two sets of hypotheses

PLEASE SHOW ANSWER WITHOUT USING EXCEL OR ANY SOFTWARE. NEED DETAILED WORKINGS OF THE ANSWER. PLEASE NOTE NO EXCEL

Female students at a certain college participate in sports with the following probabilities: Soccer = 0.32 Basketball = 0.22 Tennis = 0.22 Both soccer and basketball = 0.06 All three sports = 0.03 Both soccer and tennis = 0.12 Both basketball and tennis = 0.05

a) Construct the associated Venn diagram with all probabilities specified. (HINT: start with the idea that Pr(S ∩ B ∩ T) = 0.03 and then work your way through the rest of the diagram). (SHOW WORK; 1 point)
Next, you select one female student at random for an interview; determine the probability she plays

2. b) At least one of the three sports

3. c) Exactly one of the three sports

4. d) Exactly two of the three sports

Coconut palm is a multiple use tree, and is consider as one of the ten most useful trees in the world. The heights of a sample of 15 full-grown coconut trees are given below in meters:

20.5, 30.1, 26.7, 22.7, 27.9, 30, 32.4, 20.7, 28.4, 25.9, 28.5, 23.8, 28, 29.4, 26.9

If the heights of all coconut trees are normally distributed, test that the mean height is greater than 25 meters.

1- What is the null hypothesis?

2- What is the alternative hypothesis?

3- What is the inference method?

4- What is the value of the test statistic?

5- What is the number of degrees of freedom of the test?

6- What is the p-value of the test?

7- What is your decision?

Question 7 options:

in a study of 140 women, the relationship between working status (full time, part time, not working).and obesity (BMI <30 or not) would be examined using which of the following statistical test
chi square
independent t test
McNemar test
paired t test

Explain with an example the process for determining the replicates number for Design of Experiments.

Please make sure to display your thought process? It is imperative to be able to follow how the answer was deduced. Please be as thorough as possible. Please address all parts of this question.

A team of medical researchers wants to estimate the malaria infection rate in a difficult-to-access jungle region of [No Name Country]. There are 80 villages in the studied part of the jungle, which can be assumed to be rather similar to each other. Each village has at least 300 inhabitants. We want to test 200 individuals for malaria. Propose a cost-efficient sampling method using one or multiple (the one that applies the most" "PROBABILITY THEORY BASED MODELS" of discrete or continuous probability distributions?

In our lecture on Planning Ahead: Sampling variability, you were introduced to a set of five (5) questions that can be used to help decide upon a relevant statistical inference procedure.

1. Identify each of the five (5) questions and answer each question based on the scenario described above.
2. Based on your answers to part a, identify which of the inference procedures covered in class is most appropriate to analyse the researcher’s data?
3. Assume the researchers for the above scenario have obtained relevant simple random sample(s). Identify (by name) the sampling distribution that underlies the statistical inference procedure named in part b. Then, give the formulae for the mean and standard deviation for the sampling distribution you have identified.

my answer to a is:

1. The first question is “what is your analysis goal?”. The analysis goal based on the scenario above is to determine if student employment has an influence on their academic success. The second question is “how many ‘samples’ or groups are you comparing?”. Based on the scenario above, the researcher is comparing a single sample of university students and each student in the sample is surveyed. The third question is “are you ‘samples’ independent or paired?”. In this scenario, the sample is independent as the data is obtained from each student each case is unrelated to the other. The fourth question is “what type of data are you collecting? Quantitative or categorical?”. Based on the scenario above, the data being collected quantitative. Both the employment status and their course grades produce a numerical value to describe the dat The last question is “what parameters are of interest?”. In the above scenario, the parameters of interest are the hours worked per week and the mean of the student’s course grades.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ?μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495495 .

In answering the questions, use ?z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490490 and 500500 ? UseTable A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score ?¯x¯ ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490490 and 500500 ? (Enter your answer rounded to four decimal places.)

a. all Hypothesis Tests must include all four steps, clearly labeled;

b. all Confidence Intervals must include all output as well as the CI itself

c. include which calculator function you used for each problem.

2. An experiment was done to see whether open-book tests make a difference. A calculus class of 48 students agreed to be randomly assigned by the draw of cards to take a quiz either by open-notes or closed-notes. The quiz consisted of 30 integration problems of varying difficulty. Students were to do as many as possible in 30 minutes. The 24 students taking the exam closed-notes got an average of 15 problems correct with a standard deviation of 2.5. The open-notes crowd got an average of 12.5 correct with a standard deviation of 3.5. Assume that the populations are approximately normal. At the 5% significance level, does this data suggest that differences exist in the mean scores between the two methods?

The following data give the weight (in kg) of all six employees of a company.

1. Construct the population distribution of the weight of the employees.

[3 marks]

2. List all the possible samples of size four (without replacement) that can be selected from this population.

[10 marks]

3. Calculate the mean for each of the samples in part (b).

[4 marks]

4. Write the sampling distribution of ?̅.

[4 marks]

5. Compute the sampling errors for the samples in part (b).