Name if the following are discrete or continuous variables. Also name if the scenario is ratio, ordinal, nominal, or interval   The different heights of children in a fourth-grade class- The divisions of the American League in Major League Baseball- The number of pennies sitting in a jar- The time taken to deliver newspapers on a delivery route- Your age relative to the average age of other students in the class- The level of pain a patient indicates on a pain scale of 1-10- The counties of Ireland- The height of a pier above or below the surface of the water- The Nation Weather Service’s classification of Hurricanes as Categories 1, 2, 3, 4, or 5- Amount of water in an Olympic Swimming Pool-

Thanks!

Name if the following are discrete or continuous variables.

Also name if the scenario is ratio, ordinal, nominal, or interval  

The different heights of children in a fourth-grade class-

2. The divisions of the American League in Major League Baseball-

3. The number of pennies sitting in a jar-

4. The time taken to deliver newspapers on a delivery route-

5. Your age relative to the average age of other students in the class-

6. The level of pain a patient indicates on a pain scale of 1-10-

7. The counties of Ireland-

8. The height of a pier above or below the surface of the water-

9. The Nation Weather Service’s classification of Hurricanes as Categories 1, 2, 3, 4, or 5-

10. Amount of water in an Olympic Swimming Pool-

1. Suppose a point is to be selected at random from the unit circle. Write the sample space associated with this random experiment.

What is the BEST statistical method to use when you want to assess the association between a variable that is in ordinal scale and multiple variables that are in ratio/interval/ordinal scale.

Use the distribution in the form of the stem-leaf plot.

Stem      Leaves

1                 1478

2              01237888

3                  189          

16/ The mid-point of the third class is

A./   32   B/   36 C/    34.5 D/   35

17/ The median is

A./   24 B/  23 C/ 25   D/ 5

18/ The relative frequency for the third class is:

A./   20%   B/  50% C/    66% D/   40%

19/ The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height from this frequency table.

Height s (in)           Frequency

70-72                            4

73-75                            6

76-78                            8

79-81                            2

A./   75.2 in   B/  76.8 in C/    74.0 in D/   77.5 in

20/ The temperatures ( in ºF ) in a room is recorded at the top of hours are

67, 68, 70 , 5, 77, 77, 78, 80, 78, 79, 74, 74. Choose best answer:

a/  It is a typo

b/  highest temperature is probably 95

c/  5 is not an outlier

d/  5 is an outlier

21/ The variance of 6 washing machines with prices:  $ 800, $784, $ 1,235, $860, $1,036 and $770 is

A/ 196.4 B/   34,295.3 C/ 26,002.7 D/ 185.2

22/ The coefficient of variation ( round to closest %) for the set of data  :

1, 3, 3, 5, 5, 6, 7, 8, 9 ,12, 15, 24  is

A   74% B/ 67% C/ 24% D/ 78 %

23/ Human body temperatures have the mean of 98.2º  and a standard deviation of 0.6º.

Amy’s temperature can be described by z = 0.9. What is her temperature?

A/ 98.2º B/ 97.8º C/   98.7º D/ 99.3º

24/ The upper bound for the outlier for the data set

-11, 14, 22, 22, 22, 23, 31, 31, 42, 44, 44, 75    is

A/  74.5 B/  75 C/ 84 D/   68

25/ The box-plot of a data with 5- point summary   2, 6, 8, 11, 18

A/is positive skewed. B/ is negative skewed.

C/ is symmetric D/ perfect skewed

Researchers use Elisa to test for Lyme disease. Lyme disease infects 0.0009 of the US population each year. The test has a detection rate of 0.98 and a false positive rate of 0.2.

a. What is the probability of a positive test?

b. What is the probability that a person with a positive result actually has Lyme disease?

1. Determine statistically which two bands are the most correlated? Explain how did you get your answer and include intermediate calculations.

1. A company is to hire two employees. They have prepared a final list of eight candidates, all of whom are equally qualified. Of these eight candidates, five are women. If the company decides to select two persons randomly from these eight candidates, what is the probability that:

1. Both candidates are women.
2. The second candidate is a woman.
3. The first candidate is a woman given that second one is a woman.

1. A is called a palindrome if it reads the same from left and right. For instance, 13631 is a
palindrome, while 435734 is not. A 6-digit number n is randomly chosen. Find the probability
of the event that
(a) n is a palindrome.
(b) n is odd and a palindrome.
(c) n is even and a palindrome.

Section 1

Tennis players often spin a racquet to decide who serves first. Th e spun racquet can land with the manufacturer’s label facing up or down. A reasonable question to investigate is whether a spun tennis racquet is equally likely to land with the label facing up or down. (If the spun racquet is equally likely to land with the label facing in either direction, we say that the spinning process is fair.) Suppose that you gather data by spinning your tennis racquet 100 times, each time recording whether it lands with the label facing up or down.

1.1.1

a. Describe the relevant long-run proportion of interest in words.

b. What statistical term is given to the long-run proportion you described in (a)?

c. What value does the chance model assert for the long-run proportion?

d. Suppose that the spun racquet lands with the label facing up 48 times out of 100. Explain, as if to a friend who has not studied statistics, why this result does not constitute strong evidence against believing that the spinning process is fair.

e. Is the result in (d) statistically significant evidence that spinning is not fair or is it plausible that the spinning process is fair?

1.Assume that the heights of adult women are normally distributed with a mean height of 160 centimeters and the standard deviation is 8 centimeters.

What percentage of individuals have heights less than 160 centimeters?

2. Find the probability that a randomly selected individual has a height greater than 176 centimeters.

3. Find the probability that a randomly selected individual has a height less than 152 centimeters.

4. Can you determine the probability that a randomly selected individual has a height greater than 180 centimeters?

Question 3 [25]
OK furniture store submit weekly records the number of customer contacts contacted per week. A sample of 50 weekly reports showed a sample mean of 25 customer contacts per week. The sample standard deviation was 5.2. (Show all your works)
a) Compute the Margin of error at 0.05 significant level
[6]
b) Provide a 95% confidence interval for the population mean.
[4]
c) Compute the Margin of error at 0.01 significant level
[6]
d) Provide a 99% confidence interval for the population mean.
[4]
e) With a 0.99 probability, what size of sample should be taken if the desired margin of error is 1.5

Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $61, $99, and $135, respectively. The production requirements per unit are as follows:

For the coming production period, the company has 250 fan motors, 360 cooling coils, and 2600 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows:

The sensitivity report is shown in the figure below.

1. Identify the range of optimality for each objective function coefficient. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
   

   	Objective Coefficient Range
   Variable	lower limit	upper limit
   E
   S
   D

2. Suppose the profit for the economy model (E) is increased by $6 per unit, the profit for the standard model (S) is decreased by $2 per unit, and the profit for the deluxe model (D) is increased by $4 per unit. What will the new optimal solution be? If required, round your answers to three decimal places. If your answer is zero, enter "0".
   

   Optimal Solution
   E
   S
   D

   
   If required, round your answer for Total Profit to two decimal places.
   
   Total Profit: $_____
   
3. Identify the range of feasibility for the right-hand-side values. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
   

   	Right-Hand-Side-Range
   Constraints	lower limit	upper limit
   Fan motors
   Cooling coils
   Manufacturing time

4. If the number of fan motors available for production is increased by 60, will the dual value for that constraint change?
   
   Yes  because the allowable increase for fan motors is_____without changing the optimal solution.

The following require calculating the probability of the specified event based on an assumed probability distribution. Remember to consider whether the event involves discrete or continuous variables.

You are measuring height of vegetation in a grassland using a Robel pole and a 5 m. radius. Based on 100 random samples from the grassland, you obtain a mean height of 0.6 m with a standard deviation of 0.04 m2.

a) What distribution is the appropriate reference for this problem?

b) Ninety percent of the samples are expected to be under what height? Use you will need to use the appropriate command in R of d<dist>, p<dist>, q<dist>, or r<dist> and use the appropriate values as arguments. Use help(command) to find out what these arguments are for your distribution, e.g., help(qbinom) will give you the help for this command.

A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chickens. 55 of the children preferred hamburger and 20 preferred chickens. Set up a 2x2 contingency table using this information and answer the following questions:

What is the probability that a randomly selected individual is an adult?

What is the probability that a randomly selected individual is a child and prefers chicken?

Given the person is a child, what is the probability that this child prefers a

hamburger?

Assume we know that a person has ordered chicken, what is the probability that this individual is an adult?

Are food preference and age statistically independent?

2) Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.

Calculate P(A and O)

Calculate P(B and O)

Calculate P(C and O)

Calculate the probability that a package was delivered on time.

If a package was delivered on time, what is the probability that it was service A?

If a package was delivered 40 minutes late, what is the probability that it was service A?

3) The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.

What is the probability that there will be exactly 3 power outages in a year?

What is the probability that there will be at least 1 power outage in a year?

What is the variance for this distribution?

What is the mean power outage for this nuclear power plant in a decade?