PSY-520 Graduate Statistics
Topic 5 – Benchmark – Correlation and Regression Project
Directions: Use the following information to complete the questions below. While APA format is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center.
This benchmark assignment assesses the following programmatic competencies: 3.1: Interpret psychological phenomena using scientific reasoning
In: Math
1. A researcher wants to determine the average given below. Describe how the researcher should apply the five basic steps in a statistical study. (Assume that all the people in the poll answered truthfully.) The average number of light bulbs per household that function as designed. Determine how to apply the first basic step in a statistical study in this situation. Choose the correct answer below. a. The population is all households. The researcher wants to estimate the average b. The population is all light bulbs that function as designed. The researcher wants to estimate the average number of light bulbs per household that function as designed. c. The population is all light bulbs that function as designed. The researcher wants to estimate the average number of light bulbs per household that do not function as designed. d. The population is all households. The researcher wants to estimate the average number of light bulbs per household that function as designed. 2. Determine how to apply the second basic step in a statistical study in this situation. Choose the correct answer below. a. The researcher should gather data about functionality from the largest sample of light bulbs about whom the researcher can gather data. b. The researcher should only gather raw data from light bulbs that function as designed. c. The researcher should gather raw data from all light bulbs. d. The researcher should only gather raw data from light bulbs that do not function as designed. 3. Determine how to apply the third basic step in a statistical study in this situation. Choose the correct answer below. a. The sample statistic of interest is the average number of light bulbs per household that function as designed. b. The sample statistic of interests is the average number of light bulbs per household that do not function as designed. c. The sample statistic of interest is the percentage of light bulbs that do not function as deigned. d. The sample statistic of interest is the percentage of light bulbs that function as designed. 4. Determine how to apply the fourth basic step in a statistical study in this situation. Choose the correct answer below. a. The researcher should use the sample statistic as an estimate for the population value of the average number of light bulbs that function as designed and then use the methods of statistics to determine how good that estimate is. b. If the percentage of light bulbs that function as designed in the sample is greater than 50%, then the researcher can be confident that all light bulbs function as designed. c. The sample statistic provides no useful information to the researcher in this situation. d. If the researcher followed correct procedures, he or she can be confident that the sample statistics is equal to the average number of light bulbs that function as designed. 5. Determine how to apply the fifth basic step in a statistical study in this situation. Choose the correct answer below. a. The researcher should use the methods of statistics to determine the quality of the estimate of the population parameter and draw conclusions based on this estimate accordingly. b. The researcher cannot draw any conclusions based on the value of the sample statistic. c. There is no way to determine how well the sample statistic estimates the population parameter. d. The researcher knows that the sample statistic is equal to the population parameter, so he or she may draw conclusions with complete confidence.
In: Math
1.5 Suppose you believe that, in general, graduates who have majored in your subject are offered higher salaries upon graduating than are graduates of other programs. Describe a statistical experiment that could help test your belief.
1.6 You are shown a coin that its owner says is fair in the
sense that it will produce the same number of
heads and tails when flipped a very large number of times.
a.Describe an experiment to test this claim.
b. What is the population in your experiment?
c. What is the sample?
d. What is the parameter?
e. What is the statistic?
f. Describe briefly how statistical inference can be used to test the claim.
1.7 Suppose that in Exercise
1.6 you decide to flip the coin 100 times.
a.What conclusion would you be likely to draw if you observed 95
heads?
b. What conclusion would you be likely to draw if you observed 55
heads?
c.Do you believe that, if you flip a perfectly fair coin 100 times,
you will always observe exactly 50 heads? If you answered “no,”
then what numbers do you think are possible? If you answered “yes,”
how many heads would you observe if you flipped the coin twice? Try
flipping a coin twice and repeating this experiment 10 times and
report the results.
1.8 Xr01-08 The owner of a large fleet of taxis is trying to estimate his costs for next year’s operations. One major cost is fuel purchase. To estimate fuel purchase, the owner needs to know the total distance his taxis will travel next year, the cost of a gallon of fuel, and the fuel mileage of his taxis. The owner has been provided with the first two figures (distance estimate and cost of a gallon of fuel). However, because of the high cost of gasoline, the owner has recently converted his taxis to operate on propane. He has measured and recorded the propane mileage (in miles per gallon) for 50 taxis.
a.What is the population of interest?
b. What is the parameter the owner needs?
c. What is the sample?
d. What is the statistic?
e. Describe briefly how the statistic will produce the kind of information the owner wants.
In: Math
1.1 In your own words, define and give an example of each of the
following statistical terms. a.
population
b. sample statistic
e.
c. parameter d.
statistical inference
1.2 Briefly describe the difference between descriptive statistics and inferential statistics.
1.3 A politician who is running for the office of mayor of a
city with 25,000 registered voters commissions a survey. In the
survey, 48% of the 200 registered voters interviewed say they plan
to vote for her. a.
What is the population of interest? b. What is the sample?
c.Is the value 48% a parameter or a statistic? Explain.
1.4 A manufacturer of computer chips claims that less than 10% of its products are defective. When 1,000 chips were drawn from a large production, 7.5% were found to be defective.
a.What is the population of interest?
b. What is the sample?
c. What is the parameter?
d. What is the statistic?
e.Does the value 10% refer to the parameter or to the statistic?
f. Is the value 7.5% a parameter or a statistic?
g. Explain briefly how the statistic can be used to make inferences about the parameter to test the claim.
1.5 Suppose you believe that, in general, graduates who have
majored in your subject are offered higher salaries upon graduating
than are graduates of other programs. Describe a statistical
experiment that could help test your belief.
1.6 You are shown a coin that its owner says is fair in the
sense that it will produce the same number of
heads and tails when flipped a very large number of times.
a.Describe an experiment to test this claim.
b. What is the population in your experiment?
c. What is the sample?
d. What is the parameter?
e. What is the statistic?
f. Describe briefly how statistical inference can be used to test the claim.
1.7 Suppose that in Exercise
1.6 you decide to flip the coin 100 times.
a.What conclusion would you be likely to draw if you observed 95
heads?
b. What conclusion would you be likely to draw if you observed 55
heads?
c.Do you believe that, if you flip a perfectly fair coin 100 times,
you will always observe exactly 50 heads? If you answered “no,”
then what numbers do you think are possible? If you answered “yes,”
how many heads would you observe if you flipped the coin twice? Try
flipping a coin twice and repeating this experiment 10 times and
report the results.
1.8 Xr01-08 The owner of a large fleet of taxis is trying to estimate his costs for next year’s operations. One major cost is fuel purchase. To estimate fuel purchase, the owner needs to know the total distance his taxis will travel next year, the cost of a gallon of fuel, and the fuel mileage of his taxis. The owner has been provided with the first two figures (distance estimate and cost of a gallon of fuel). However, because of the high cost of gasoline, the owner has recently converted his taxis to operate on propane. He has measured and recorded the propane mileage (in miles per gallon) for 50 taxis.
a.What is the population of interest?
b. What is the parameter the owner needs?
c. What is the sample?
d. What is the statistic?
e. Describe briefly how the statistic will produce the kind of information the owner wants.
In: Math
3. The heights of female students attending a sixth form college have a mean of 168 cm and standard deviation of 4.5 cm. The heights can be modeled by a normal distribution: a. Find the probability that the height of a randomly selected female student attending this college is less than 172.5 cm? b. Find the probability that the mean height of a random sample of 11 female students from this college exceeds 172 cm?
In: Math
Employees from Company A and Company B both receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.05 level of significance? Write out the hypothesis and explain the testing procedure.
In: Math
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Part 2 – SPSS APPLICATION from this week’s assigned readings and presentations (28 pts) |
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Problem Set 1: The independent-samples t test (7 pts) Research Scenario: A clinical psychologist is studying whether there is a difference between veterans diagnosed with PTSD and veterans without PTSD in reduction of anxiety after aerobic exercise. All veterans in this study agree to complete 30 minutes of aerobic exercise 5 days a week for 4 weeks and began with similar levels of reported anxiety. Scores shown are calculated difference scores in anxiety, with higher scores indicating more of a reduction in anxiety (scale measurement). Using this table, enter the data into a new SPSS data file and run an independent samples t test to test whether aerobic exercise differentially affects anxiety in veterans with and without PTSD. Remember to name and define your variables under the “Variable View,” then return to the “Data View” to enter and analyze the data. Remember, data will be entered differently than in a paired samples t-test. Specifically, you will have one variable (“Group”), with 0 = no PTSD and 1 = PTSD. The other variable is “Change”. Thus, data will not be entered exactly as shown below. |
|
NoPTSD |
PTSD |
|
24 |
25 |
|
23 |
23 |
|
22 |
27 |
|
30 |
19 |
|
31 |
22 |
|
30 |
13 |
|
38 |
18 |
|
25 |
28 |
|
33 |
21 |
|
38 |
31 |
|
Problem Set 2: Pearson’s correlation (7 pts) Research Scenario: Is there a positive relationship between grit and dieting success? A researcher examined this issue by having people complete a grit inventory using a Likert-based scale (range 1 – 7), where higher numbers indicate more “grit”. Dieting success was measured using a likert-based inventory as well, with higher numbers indicating more success (range 1-7). Enter the data shown here into SPSS to run an analysis to test whether increased grit is associated with higher dieting success.
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Note: Please solve it by text not in hand written form.
In: Math
An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the color index, or B−V index, and distance (in light years) from Earth for 30 stars. The color index of a star is the difference in the light absorption measured from the star using two different light filters (a B and a V filter). This then allows the scientist to know the star's temperature and a negative value means a hot blue star. A light year is the distance light can travel in 1 year, which is approximately 5.9 trillion miles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places.
B-V index Distance (ly)
1.1 1380
0.4 556
1.0 771
0.5 304
1.4 532
1.0 751
0.5 267
0.8 229
0.5 552
0.2 896
1.5 1819
0.5 381
0.5 257
1.1 541
0.7 133
0.5 300
0.0 985
0.4 525
1.0 408
1.1 1367
1.07 2848
1.1 128.9
1.12 1766.2
0.64 186.5
0.87 8269.2
0.19 828.9
1.03 153
0.55 223.6
1.39 963.9
0.89 91.7
R=
In: Math
1. T F The number of defects on a product produced by a process is distributed as a Poisson distribution.
2. T F For large binomially distributed populations and small samples you can use sampling without replacement
3. T F Given a triangular distribution with minimum 2, maximum 8 and mode 7, the probability of being smaller than 7 is greater than 60%
4. T F The hypergeometric distribution describes sampling without replacement
5. T F The relative frequency of a value is the proportion of times the value occurs.
6. T F The permutation of n numbers is always smaller than the combination of the same n numbers, taken the same number of times
7. T F The intersection of two events is greater than zero when they are mutually exclusive
8. T F The probability of rolling a 6 with a fair six sided die is 1/6.
9. T F The product of the probability of two independent events is called conditional probability.
10. T F When we use both a beta and a triangular distribution to represent a variable, the probability of a low value will always be grater with the triangular distribution
In: Math
Alper, Beatta, and Grandma each pick five cards from a shuffled
standard deck. Alper replaces the card and reshuffles each time he
picks. Beatta picks from the deck without replacement. Grandma
repeatedly picks the top card from the deck and puts it back on the
top of the deck. Count an ace as 14, a king as 13, and so on. Let
X,Y,Z be the sum of the numbers Alper, Beatta, and Grandma get,
respectively. Which of X,Y,Z has or have the largest
expected value?
Which of X,Y,Z has or have the largest variance?
Would someone please help me out with correct and detailed answer please?
In: Math
1. A survey administered to a random sample from a local grocery store finds that political party is related to whether or not they favor an increase in sales tax, leading to a news story: Republicans support proposed tax increase. This is an example of what type of statistic?
2. What are measures of central tendency? When is each appropriate? What influences each measure of central tendency? (ex. What is affected by every score in the distribution? If you change only the highest score, what measure does that change?). What is the preferred measure of central tendency for a skewed variable? What is the purpose of measures of central tendency?
In: Math
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here:
| Cabinetmaker 1 | Cabinetmaker 2 | Cabinetmaker 3 | |
| Hours required to complete all the oak cabinets | 47 | 40 | 27 |
| Hours required to complete all the cherry cabinets | 64 | 52 | 36 |
| Hours available | 40 | 30 | 35 |
| Cost per hour | $34 | $41 | $52 |
a. Formulate a linear programming model that can be used
to determine the proportion of the oak cabinets and the proportion
of the cherry cabinets that should be given to each of the three
cabinetmakers in order to minimize the total cost of completing
both projects.
| Let | O1 = proportion of Oak cabinets assigned to cabinetmaker 1 |
| O2 = proportion of Oak cabinets assigned to cabinetmaker 2 | |
| O3 = proportion of Oak cabinets assigned to cabinetmaker 3 | |
| C1 = proportion of Cherry cabinets assigned to cabinetmaker 1 | |
| C2 = proportion of Cherry cabinets assigned to cabinetmaker 2 | |
| C3 = proportion of Cherry cabinets assigned to cabinetmaker 3 |
| Min | __________O1 | + | __________O2 | + | __________O3 | + | __________C1 | + | __________C2 | + | __________C3 | |||
| s.t. | ||||||||||||||
| __________O1 | __________C1 | ≤ | __________ | Hours avail. 1 | ||||||||||
| __________O2 | + | __________C2 | ≤ | __________ | Hours avail. 2 | |||||||||
| __________O3 | + | __________C3 | ≤ | __________ | Hours avail. 3 | |||||||||
| __________O1 | + | __________O2 | + | __________O3 | = | __________ | Oak | |||||||
| __________C1 | + | __________C2 | + | __________C3 | = | __________ | Cherry | |||||||
| O1, O2, O3, C1, C2, C3 ≥ 0 | ||||||||||||||
b. Solve the model formulated in part (a). What proportion of the oak cabinets and what proportion of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost of completing both projects? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places.
| Cabinetmaker 1 | Cabinetmaker 2 | Cabinetmaker 3 | |
|---|---|---|---|
| Oak | O1 = _______ | O2 = _______ | O3 = _______ |
| Cherry | C1 = _______ | C2 = _______ | C3 = _______ |
Total cost = $ __________
c. If Cabinetmaker 1 has additional hours available,
would the optimal solution change? YES OR NO
Explain.
d. If Cabinetmaker 2 has additional hours available,
would the optimal solution change? YES OR NO
Explain.
e. Suppose Cabinetmaker 2 reduced its cost to $38 per
hour. What effect would this change have on the optimal solution?
If required, round your answers for the proportions to three
decimal places, and for the total cost to two decimal
places.
| Cabinetmaker 1 | Cabinetmaker 2 | Cabinetmaker 3 | |
|---|---|---|---|
| Oak | O1 = _______ | O2 = _______ | O3 = _______ |
| Cherry | C1 = _______ | C2 = _______ | C3 = _______ |
Total cost = $ __________
Explain.
In: Math
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attractive properties though it is more expensive to produce than standard plastics. The accompanying data on melting point (°C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in an article.
180.6 181.7 180.8 181.5 182.6 181.6 181.2 182.1 182.2 180.4 181.8 180.4
Compute the following. (Round your answers to two decimal places.)
(a) the sample range
(b) the sample variance s^2 from the definition [Hint: First subtract 180 from each observation.]
(c) the sample standard deviation
(d) s^2 using the shortcut method
In: Math
La Jolla Beverage Products is considering producing a wine cooler that would be a blend of a white wine, a rose wine, and fruit juice. To meet taste specifications, the wine cooler must consist of at least 50% white wine, at least 20% and no more than 30% rose, and exactly 20% fruit juice. La Jolla purchases the wine from local wineries and the fruit juice from a processing plant in San Francisco. For the current production period, 10000 gallons of white wine and 8000 gallons of rose wine can be purchased; an unlimited amount of fruit juice can be ordered. The costs for the wine are $1 per gallon for the white and $1.5 per gallon for the rose; the fruit juice can be purchased for $0.5 per gallon. La Jolla Beverage Products can sell all of the wine cooler it can produce for $2.5 per gallon.
a. Is the cost of the wine and fruit juice a sunk cost
or a relevant cost in this situation? Explain.
b. Formulate a linear program to determine the blend of the three ingredients that will maximize the total profit contribution. Solve the linear program to determine the number of gallons of each ingredient La Jolla should purchase and the total profit contribution it will realize from this blend. If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.
| Let W = gallons of white wine | |
| Let R = gallons of rose wine | |
| Let F = gallons of fruit wine |
| Max | __________W | + | _________R | + | __________F | |||
| s.t. | ||||||||
| __________W | + | __________R | + | __________F | ≥ | __________ | % white | |
| __________W | + | __________R | + | __________F | ≥ | __________ | % rose minimum | |
| __________W | + | __________R | + | __________F | ≤ | __________ | % rose maximum | |
| __________W | + | __________R | + | __________F | = | __________ | % fruit juice | |
| __________W | ≤ | __________ | Available white | |||||
| __________R | ≤ | __________ | Available rose | |||||
| W, R, F ≥ 0 | ||||||||
| Optimal Solution: | |
|---|---|
| W | __________ |
| R | __________ |
| F | __________ |
Profit Contribution = __________
c. If La Jolla could obtain additional amounts of the white wine, should it do so? YES OR NO
If so, how much should it be willing to pay for each additional gallon, and how many additional gallons would it want to purchase?
d. If La Jolla Beverage Products could obtain additional amounts of the rosé wine, should it do so? YES OR NO.
If so, how much should it be willing to pay for each additional
gallon, and how many additional gallons would it want to
purchase?
e. Interpret the shadow price for the constraint corresponding to the requirement that the wine cooler must contain at least 50% white wine. What is your advice to management given this shadow price?
f. Interpret the shadow price for the constraint
corresponding to the requirement that the wine cooler must contain
exactly 20% fruit juice. What is your advice to management given
this shadow price?
In: Math
1. An impartial judge of a local garden competition collects scores from two groups of judges on what he suspects to be the number one garden. He finds the first group (n = 5) has a mean score of 76. The second group (n = 3) has a mean score of 91. So that he may declare the final score, what is the weighted mean of these two groups?
2. A social scientist measures the number of minutes (per day) that a small hypothetical population of college students spends online. Student Score Student Score A 94 F 96 B 88 G 25 C 74 H 61 D 88 I 82 E 98 J 98
(a) What is the range of data in this population? min
(b) What is the IQR of data in this population? min
(c) What is the SIQR of data in this population? min
(d) What is the population variance?
(e) What is the population standard deviation? (Round your answer to two decimal places.) min
3. A sociologist records the annual household income (in thousands of dollars) among a sample of families living in a high-crime neighborhood. Locate the lower, median, and upper quartiles for the times listed below. Hint: First arrange the data in numerical order.
a) lower quartile thousand dollars
b) median thousand dollars
c) upper quartile thousand dollars
42 22 46 33 37 32 37 47 51 25
4. A theme park owner records the number of times the same kids from two separate age groups ride the newest attraction. Age 13–16 Time Age 17–21 Time 1 10 1 4 2 9 2 3 3 3 3 7 4 1 4 4 5 10 5 8 6 3 6 1 7 8 7 2 8 9 8 5 9 6 9 4 10 5 10 2 Using the computational formula, for the age group of 13–16? (Round your answers for variance and standard deviation to two decimal places.) what is the
a) SS
b) sample variance
c) standard deviation
In: Math