105. A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.

a. i. x = __________ ii. sx = __________ iii. n = __________ iv. n – 1 = __________

b. Define the random variable X in words.

c. Define the random variable X in words. d. Which distribution should you use for this problem? Explain your choice.

e. Construct a 95% confidence interval for the population mean length of time.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

f. What does it mean to be “95% confident” in this problem?

A concrete mix must withstand an average compressive stress of more than 1,300 KN / m2. The mixture will not be used unless we have sufficient evidence that the specification is being met. Assume that effort is a normally distributed random variable with a standard deviation of 60. A sample of 20 specimens is taken:

1. 1. Clearly state the null and alternative hypothesis.
2. 2. With the evidence provided, would you use the mixture? Justify. Calculate the P-Value of the test.
3. 3. Calculate by hand, the probability of making a type II error if the mean compressive stress was 1325 KN / m2. Explain in your words what it means.

3. (No computer output is accepted) A typical person in America has 155 friends in Facebook, 210 followers in Instagram and 155 followers in Twitter according to USA Tomorrow. A random sample of 30 people is selected and the following summary statistic are obtained. (Assume that the variables are normally distributed.)

Sample Mean for Facebook is 120.7
Sample Mean for İnstagram is  210.3.
Sample Mean for Twitter is 154.5

Sample Standard Deviation for Facebook is 5.2
Sample Standard Deviation for İnstagram is 7.85
Sample Standard Deviation for Twitter is 19

a)   Construct a 99% two-sided confidence interval for the mean number of friends in Facebook for all people in America.

b)   Construct a 99% two-sided confidence interval for mean number of followers in Instagram for all people in America.

c) Construct a 99% two-sided confidence interval for the mean number of followers in Twitter for all people in America.

d) Does this sample support the claim of USA Tomorrow? Explain your answer.

(Use 4 significant digits in your results. For example, if your answer is 20/7, write 2.8571. Moreover, do not leave the solution as 20/7. and show your answers in detail)

"Three Sample ANOVA QB"

Researcher wants to compare test performance for tests printed on three different colors of paper; Red, Green, and the Standard White. The researcher selects a sample of 11 individuals and has each individual take one test on Red paper, another test on Green paper, and a third test on the Standard White paer. The data are listed below. The researcher wants to minimize the probability of making a Type I error.

   Red Green White   
90 88 86
89 87 85
88 86 84
87 85 83
86 84 82
85 83 81
84 82 80
83 81 76
82 80 78
81 79 77
    80 78 79   

Means 85 83 81 Grand Mean = 83

2)What is the correct observed test statistic value for this statistical test of the means (Round to two decimal places)?

3) What is the correct critical value for this statistical test of the means?

6) conduct post-hoc analysis using Tukey’s HSD. What is the critical value?

7)what is the value of Tukey’s HSD for comparing Red paper to Green paper (Round to two decimal places)?

8)what is the value of Tukey’s HSD for comparing Red paper to White paper (Round to two decimal places)?

9)what is the value of Tukey’s HSD for comparing Green paepr to White paper (Round to two decimal places)?

Z Corporation has taxable income of $100,000 in 2020 after properly accounting for all the following items on the tax return. In reviewing the tax workpapers you discover the following notations. Indicate for each of the following transactions, what necessary adjustment to taxable income that is needed to determine the current E & P.

Label your answers A-E and indicate the dollar amount for each adjustment. If the adjustment is a negative one, enclose the amount in brackets. If no adjustment is needed, state None.

A. During 2020, the company paid $21,000 in federal income taxes

B. During 2020, the company elected to expense $40,000 under Section 179   

C. In 2020, the company received $1,000 in tax-exempt income

D. In 2020, the company paid $6,000 in business meals.

E. In 2020, the company had $5,000 in capital gains. From 2019, they had a $4,000 capital loss carryforward which they could utilize in 2020.

Learning Objective: Explain key characteristics of nonverbal communication.

Assignment: First, watch the YouTube video “10 Surprising Ways to Offend People in Other Countries” (https://www.youtube.com/watch?v=UTE0G9amZNk). Then, discuss in detail three types of nonverbal communication -- chronemics, facial expressions, and body movements -- as highlighted in the video. Define the terms and use the video to help contrast nonverbal meaning between and among cultures.

Guidelines:

Write a standard, five paragraph essay (introduction, three body paragraphs, and a conclusion).

Use sentences and formal, standard English.

Submit essay as a Microsoft Word file (.doc, .docx). Do NOT paste it within the textbox.

Additional research is not required. However, if sources are used, acknowledge them appropriately.

1) Give 2 examples of studies that can use a t-test for independent samples in your area of study or interest.

2) Give 2 examples of studies that can use a t-test for dependent samples in your area of study or interest.

3) What are TWO interesting insights you know about hypothesis testing?