A chemist measures the haptoglobin concentration (in grams per litre) in the blood serum from a random sample of 11 healthy adults. The concentrations are assumed to be normally distributed and are given below.

At a 1% level of significance, perform a statistical test to see if there is evidence that the mean haptoglobin concentration in adults is less than 1.8 grams per litre, by answering the following parts.

1.1 (.8 marks)

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 49% of all such batches contain no defective components, 27% contain one defective component, and 24% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.

(b) One of the two tested components is defective. [Hint: Draw a tree diagram with three first-generation branches for the three different types of batches.]

Consider two models that you are to fit to a single data set involving three variables: A, B, and C.

Model 1 : A ~B

Model 2 : A ~B + C

(a) When should you say that Simpson’s Paradox is occuring?

A. When Model 2 has a lower R2 than Model 1.

B. When Model 1 has a lower R2 than Model 2.

C. When the coef. on B in Model 2 has the opposite sign to the coef. on B in Model 1.

D. When the coef. on C in Model 2 has the opposite sign to the coef. on B in Model 1.

(b) True or False: If B is uncorrelated with A, then the coefficient on B in the model A ~ B must be zero.

(c) True or False: If B is uncorrelated with A, then the coefficient on B in a model A ~ B+C must be zero.

(d) True or False: Simpson’s Paradox can occur if B is uncorrelated with C.

3.4- Let Y1 = θ0 + ε1 and then for t > 1 define Yt recursively by Yt = θ0 + Yt−1 + εt. Here θ0 is a constant. The process {Yt} is called a random walk with drift.

(c) Find the autocovariance function for {Yt}.

Assignment
(1). In a city 25% of the people reads punch newspaper, 20% reads guidance. newspaper, 13% reads times newspaper, 10% reads both punch and guidance , 8% reads punch and time and 4% reads all three. If a person from this city is selected at random, what is the probability that he or she does not read any of this papers?
(2). In a community 32% of the population are male cassava farmers and 27% are female cassava farmers. what percentage of this community are cassava farmers?

18. A group of Industrial Organizational psychologists wanted to test if giving a motivational speech at the end of a meeting would encourage office workers to have a higher output to their work based on the numbers of sales each worker made. The group tested 10 participants that were in two conditions where one meeting ended in a motivational speech and another were no motivational speech was given. Here are the number of sales that was produced by the 10 participants for both conditions:

Yes speech: 2, 6, 1, 9, 3, 12, 8, 0, 5, 1

No speech: 3, 0, 5, 10, 1, 8, 2, 1,9, 11

Use the four steps of hypothesis testing to find out if there is a significant difference between the two groups, using APA format to answer the question.

20. Run the same data from question 19 (and the same criteria) using a repeated measures test.

a. Perform the test and report results (show ALL work)

b. Explain what the difference in results is due to.

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found to be 110​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct a 90​% confidence interval about mu if the sample​ size, n, is 23. ​(b) Construct a 90​% confidence interval about mu if the sample​ size, n, is 27. ​(c) Construct a 95​% confidence interval about mu if the sample​ size, n, is 23. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 119 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X ~ N( 119 , 15 ) b. Find the probability that a randomly selected person's IQ is over 113. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 2% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR:

Give an example of a discrete distribution which has finite first and second moments, but the third moment does not exist.

For a normal population with a mean equal to 77 and a standard deviation equal to 14, determine the probability of observing a sample mean of 85 or less from a sample of size 8.

P (x less than or equal to 85) =

If i can have the chart filled out with work for my understanding. I would greatly appreciate it.

An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of an apartment, as defined by square footage. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the data below.

Apartment         Monthly Rent ($)       Size (Sq. Feet)

       1                           950                               850

       2                        1,600                            1,450

       3                        1,200                            1,085

       4                        1,500                            1,232

       5                           950                               718

       6                        1,700                            1,485

       7                        1,650                            1,136

       8                           935                               726

       9                           875                               700

     10                       1,150                               956

     11                        1,400                            1,100

     12                        1,650                            1,285

     13                        2,300                            1,985

     14                        1,800                            1,369

     15                        1,400                            1,175

     16                        1,450                            1,225

     17                        1,100                            1,245

     18                        1,700                            1,259

     19                        1,200                            1,150

     20                        1,150                               896

     21                        1,600                            1,361

     22                        1,650                            1,040

     23                        1,200                               755

     24                           800                            1,000

     25                        1,750                            1,200

Excel output for this problem is given below:

4. At the 0.05 level of significance, is there evidence of a linear relationship between the size of the apartment and the monthly rent? Answer using the Excel output given above.

Measures of Average: U.S. Census Bureau

The U.S. Census Bureau reports the median family income in its summary of census data.

a) Why do you suppose it uses the median instead of the mean?

b) What might be the disadvantages of reporting the mean?

Measures of Variation: MP3 Player Life Span

A company selling a new MP3 player advertises that the player has a mean lifetime of 5 years. If you were in charge of quality control at the factory, would you prefer that the standard deviation of lifespans of the players you produce be 2 years or 2 months? Why?

1. Assuming a normal distribution with a mean of 5 and standard deviation of 1.2, what is the P(X = 6)?
   1. 0
   2. 0.2033
   3. -0.8333
   4. 0.8333
      
      
2.   Assuming the expected value of a distribution is 4 and the standard deviation is 0.85, what would be the expected value if a constant of 1 added to each value of x?
   1. 4.00
   2. 4.85
   3. 5.00
   4. 5.85
      
      
3. What distribution would you use if you want to find the expected number of heads when you flip a coin 100 times?
   1. Normal
   2. Uniform
   3. Geometric
   4. Binomial
      
      
4.   What distribution would you use if you want to find the expected number of times you have to roll a die until you get a 6?
   1. Normal
   2. Uniform
   3. Geometric
   4. Binomial
      
5.   What is the expected number of times you will get heads if you flip a fair coin (50/50 chance of heads or tails), if you flip the coin 5,000 times?
   1. 0
   2. 50
   3. 2500
   4. 5000

A study of the career paths of hotel general managers sent questionnaires to an SRS of 250 hotels belonging to major U.S. hotel chains. There were 127 responses. The average time these 127 general managers had spent with their current company was 8.92 years. (Take it as known that the standard deviation of time with the company for all general managers is 2.8 years.)

(a) Find the margin of error for a 90% confidence interval to estimate the mean time a general manager had spent with their current company: years

(b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: years

(c) In general, increasing the confidence level the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)

Consider your dissertation research interests. Identify one categorical/nominal scale IV with more than 2 categories, and three DVs that are measured on continuous scales. Think of DV measures that probably are moderately correlated with each other because they are measuring different components of the same or similar concepts (e.g., three different measures of academic performance). What information would a one-way MANOVA provide you? What more would you want to know if you get significant results in the MANOVA? Why would this be significant to your research? Please type about a 200 word response and use IQ as as the topic. Thanks