Think of a problem dealing with two variables (Y and X) that you may be interested in. Share your problem and discuss why a regression analysis could be appropriate for this problem. Specifically, what statistical questions are you asking? You should describe the data collection process that you are proposing but you do not need to collect any data.

The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older.

Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use  = .05. Use Table 12.4.

Compute the value of the X2 (Chi2) test statistic (to 2 decimals).????

b) Using the total sample of 500, estimate the percentage of people who sleep less than 6, 6 to 6.9, 7 to 7.9, and 8 or more hours on weeknights (to 1 decimal).

A study was conducted that measured the total brain volume (TBV) (in mm) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients ("SOCR data oct2009," 2013). Is there enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal? Test at the 10% level.

Table #9.3.5: Total Brain Volume (in mm) of Normal Patients

Table #9.3.6: Total Brain Volume (in mm) of Schizophrenia Patients

1. Find the critical t-value(s) for a one sample t-test given: α = 0.01 n = 12 one-tailed test (lower-tailed critical region)

a. 2.130 and -2.130

b. 3.103 and -3.103

c.-2.718

d. -2.567

e. 2.998

2.

Find the critical t-value(s) for a one sample t-testgiven:

α = 0.05

df = 26

one-tailed test (upper-tailed critical region)

a. 2.042 and -2.042

b.-1.812

c. 1.706

d. 3.241

e. -1.339

3. What decision you would make regarding the null hypothesis (reject or fail to reject (i.e., retain)) given the following scenario in a one sample t-test?

α = 0.05

p value = 0.022

a. reject the null hypothesis

b. fail to reject the null hypothesis

4. What decision you would make regarding the null hypothesis (reject or fail to reject (i.e., retain)) given the following scenario in a one sample t-test?

α = 0.01

p value = 0.524

a. reject the null hypothesis

b. fail to reject the null hypothesis

5. What decision you would make regarding the null hypothesis (reject or fail to reject (i.e., retain)) given the following scenario in a one sample t-test?

α = 0.01

p value = 0.005

a. reject the null hypothesis

b. fail to reject the null hypothesis

6. What decision you would make regarding the null hypothesis (reject or fail to reject (i.e., retain)) given the following scenario in a one sample t-test?

α = 0.05

p value = 0.232

a. reject the null hypothesis

b. fail to reject the null hypothesis

(EXCEL) DATA 1 :

THE QUESTIONS :

Q1\ The value of the test statisic ?

Q2\ The value of the p value of the test ?

Q3\ What is the H0 rejection region for the testing at the 1% level of significance ? t > ____

Q4/ interpret the result based on your Excel Outputs .

_________________________________________________________________

(EXCEL) DATA 2:

Group 1 Group 2 Group 3 Group 4

44 54 55 44

73 65 78 42

71 79 86 74

60 69 80 42

62 60 50 38

THE QUESTIONS :

Q1\ The value of the test statisic ?

Q2\ The value of the p value of the test ?

Q3\ What is the H0 rejection region for the testing at the 5% level of significance ? F >= ____

Q4/ interpret the result based on your Excel Outputs .

The number of peanut M&Ms in a 2 ounce package is normally distributed with a mean of 28 and standard deviation 2; The number of Skittles in a 2 ounce package is normally distributed with a mean of 60 and standard deviation 4.

Questions 1-3: Suppose that I purchase two 2-ounce packages of peanut M&Ms and one 2-ounce package of Skittles.

1. Let X= the total number of pieces of candy in all three bags combined. What is the distribution of X?

2. What is the probability that the total number of pieces of candy in all three bags combined is less than 110?

3. What is the probability that the total number of M&Ms (in both bags combined) is greater than the number of Skittles?

Assessment 3 – Graphical LP                                                                         

You are given the following linear programming problem.

            Maximize Z =.            $46X1 + $69X2

                        S.T.                  4X1 + 6X2      < 84

                                                2X1 + 1 X2     > 20

                                                4X1                 < 60

Using graphical procedure, solve the problem. (Graph the constraints and identify the region of feasible solutions). What are the values of X1, X2 ,S1, S2, S3, and the value of the objective function (Z) at optimum? If there are multiple optimum solutions, please give two of the optimum solutions.

Optimum solution 1:

X1 =                X2 =                S1 =                 S2 =                 S3 =                 Z =                 

Optimum solution 2: (if there is a second optimum solution)

X1 =                X2 =                S1 =                 S2 =                 S3 =                 Z =                 

Find the mean, median, and mode of the following data: 0.38, 0.52, 0.55, 0.32, 0.37, 0.38, 0.38, 0.35, 0.29, 0.38, 0.28, 0.39, 0.40, 0.38, 0.38, 0.38 Mean: Median: Mode:

Given the following data and Standard Deviation, calculate the %CV: 26, 52, 37, 22, 24, 45, 58, 28, 39, 60, 25, 47, 23, 56, 28 SD = 14.0

A fair coin is tossed repeatedly until it has landed Heads at least once and has landed Tails at least once. Find the expected number of tosses.

Heights of 10 year olds. Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. Round all answers to two decimal places.

1. What is the probability that a randomly chosen 10 year old is shorter than 57 inches?

2. What is the probability that a randomly chosen 10 year old is between 61 and 63 inches?

3. If the shortest 15% of the class is considered very tall, what is the height cutoff for very tall?  inches

4. What is the height of a 10 year old who is at the 24 th percentile?  inches

Using dataset "PlantGrowth" in R (r code)

Construct a 95% confidence interval for the true mean weight.

Interpret the confidence interval in in the context of the problem.

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 6 inches.

(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)

(b) If a random sample of eighteen 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)

(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much higher because the mean is smaller for the x distribution. The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution.

1. Define the following terms:

A. Contingency table

B. Chi-square test

2. List the assumptions required to perform a chi-square test?

The below age variable was inputted into SPSS and the descriptive statistics output generated. I did the interquartile range (39) to try and answer Question #4: Are there outliers among the values of age? provide a rationale for your answer. need help determining the Q1, Q3 if this is the correct approach to answer this questions and respond to what's the rationale?

Age variable
42
41
56
78
86
49
82
35
59
37

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 84 students in the highest quartile of the distribution, the mean score was x = 178.30. Assume a population standard deviation of σ = 7.47. These students were all classified as high on their need for closure. Assume that the 84 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score μ on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)