In a test of the hypothesis that the population mean is smaller than 50, a random sample of 10 observations is selected from the population and has a mean of 47.0 and a standard deviation of 4.1. Assume this population is normal.

a) Set up the two hypotheses for this test. Make sure you write them properly.

b) Check the assumptions that need to hold to perform this hypothesis test.

c) Calculate the t-statistic associated with the sample.

d) Graphically interpret the p-value for this test, that is, i) draw a (nice) graph with a t-distribution (remember of the number of degrees of freedom) ii) locate on the graph the t-statistic you found in part (c) iii) mark the P-value on the graph

e) Calculate the P-value for this test.

f) Statistically interpret the P-value for this test.

g) Let the level of significance α = 2.5%. Using P-value, make a conclusion for your test (write a complete sentence for full credit).

h) Let the level of significance α = 2.5%. Find the related critical value tα.

i) What is the rejection region (RR) implied by α = 2.5% ?

j) Draw the RR on your graph on page 1, part (d).

k) Using the RR, make a conclusion for your test (write a complete sentence for full credit).

Suppose x has a normal distribution with mean μ = 28 and standard deviation σ = 4.

a) Describe the distribution of x values for sample size n = 4. (Round σ_x to two decimal places.)

b) Describe the distribution of x values for sample size n = 16. (Round σ_x to two decimal places.)

c) Describe the distribution of x values for sample size n = 100. (Round σ_x to two decimal places.)

d) How do the x distributions compare for the various samples sizes?

I. The means are the same, but the standard deviations are decreasing with increasing sample size.

II. The standard deviations are the same, but the means are decreasing with increasing sample size.    

III. The means and standard deviations are the same regardless of sample size.

VI. The means are the same, but the standard deviations are increasing with increasing sample size.

V. The standard deviations are the same, but the means are increasing with increasing sample size.

1. Police response time to an emergency call is the difference between the time the call is first received and the time a patrol car arrives at the scene. Over along period of time, it has been determined that the police response time is normally distributed with a mean of 8.4 minutes and a standard deviation of 7 minutes. For a randomly received emergency call, what is the probability that the response time will be:
   1. Between 5 and 10 minutes
   2. Less than 5 minutes
   3. More than 10 minutes

QUESTION 1

1. Which of the following scenarios are most suitable for the chi-square test for difference in proportions?
   Hint: There are 3 correct answers.

   	a.	You want to know whether there is any difference between the average number of females and the average number of males who prefer working for a boss of the opposite gender as compared to a boss of the same gender.
   	b.	You are curious to find out if there is any difference in the average incomes among the U.S., Canada and the U.K.
   	c.	You wonder whether there is any difference in the proportions of smokers between female high school students and male high school students.
   	d.	You are interested in finding out whether the proportions of students who agree that NAU should increase its tuition further are the same across freshmen, sophomores, juniors and seniors.
   	e.	You are interest in finding out whether the percentages of PCs that break down within the first month are the same across five different manufacturers.
   	f.	You want to know whether the percentage of republicans who favor a tax cut is higher than the percentage among democrats.

QUESTION 2

1. Which of the following scenarios are most suitable for the chi-square test for independence?
   Hint: There are 2 correct answers.

   	a.	You want to know if there is any connection between a person’s hair color and eye color.
   	b.	You want to know whether there is any difference between the average number of females and the average number of males who prefer working for a boss of the opposite gender as compared to a boss of the same gender.
   	c.	You are curious to find out if the variations of smokers are the same across freshmen, sophomores, juniors and seniors at NAU.
   	d.	You wonder whether political party affiliation is related to gender.
   	e.	You are curious to find out if there is any difference in the average incomes among the U.S., Canada and the U.K.
   	f.	You want to know whether median income of republicans are higher than the median income of democrats.

QUESTION 3

1. Which of the following scenarios are most suitable for the Z test for difference in two proportions?
   Hint: There are 2 correct answers.

   	a.	You are interested in finding out whether the proportions of students who agree that NAU should increase its tuition further are the same across freshmen, sophomores, juniors and seniors.
   	b.	You are interest in finding out whether the percentages of PCs that break down within the first month are the same across five different manufacturers.
   	c.	You wonder whether political party affiliation is related to gender.
   	d.	You want to know if there is any connection between a person’s hair color and eye color.
   	e.	You wonder whether there is any difference in the proportions of smokers between female high school students and male high school students.
   	f.	You want to know whether the percentage of republicans who favor a tax cut is higher than the percentage among democrats.
   	g.	You are curious to find out if there is any difference in the average incomes among the U.S., Canada and the U.K.
   	h.	You want to know whether there is any difference between the average number of females and the average number of males who prefer working for a boss of the opposite gender as compared to a boss of the same gender.

QUESTION 4

1. When should the Marascuilo procedure be used?

   	a.	To find out if there is any difference in any pair of population proportions when one fails to reject the chi-square test for two proportions.
   	b.	To find out if there is any difference in any pair of population proportions once the chi-square test for more than two proportions is rejected.
   	c.	To find out if there is any difference in any pair of population porportions when one fails to reject the chi-square test for more than two proportions.
   	d.	To find out if there is any difference in any pair of population proportions once the chi-square test for two proportions is rejected.

QUESTION 5

1. The computation and operation procedure of the chi-square test for independence is exactly the same as those of which of the following?
   One correct answer.

   	a.	one-way ANOVA F test
   	b.	Z test for difference in two proportions
   	c.	Tukey-Kramer procedure
   	d.	Chi-square test for difference in more than two proportions
   	e.	Marascuilo procedure
   	f.	Z test for difference in two means

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.