**PSYC 354 Homework 1 – Introduction to Statistics Assignments**

When submitting this file, be sure the filename includes your full name, course and section.

Be sure you have reviewed this module/week’s lesson and presentations before proceeding to the homework exercises. Number all responses. Review the “Homework Instructions: General” document for an example of how homework assignments must look.

**All Questions**

**Part I: Concepts**

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

Fill in the blank with the appropriate word or words.

- A statistic that uses sample data to make general estimates about the larger population is statistic.
- A statistic that summarizes a group of numbers is a(n) statistic.
- A(n) is a set of observations drawn from the larger group of interest.
- The large group about which you want to know something is called .
- A five-star rating system for movies is a variable at the level of measurement.
- A person’s religious preference is a variable at the level of measurement.
- A(n) variable is a variable that meets the criteria for an interval and ratio variable.
- Discrete values that the independent variable can take on are called the of the independent variable.
- A variable that is manipulated to determine its effects on another variable is a(n)

- variable.

- A(n) variable makes it impossible to determine whether the independent variable is the cause of changes in the dependent variable.
- is the process of drawing conclusions about whether or not a particular relation between variables is supported by the data.
- The hallmark of a(n) is the random assignment of participants to conditions

- so that cause and effect can be discovered.

- When each participant has the same chance of being assigned to the various levels of the manipulation, they are said to be to conditions.
- Each participant experiences all levels of the independent variable in a(n) design.
- Participants experience only one level of the independent variable in a(n) design.

### PSYC 354 Homework 1 – Introduction to Statistics Assignments

**Answer the following questions:**

**Question 1a-1b**

A health psychologists decides to study the effects of living region (rural, suburban, urban) on the number of extra-curricular activities of residents.

**1-a)** What would the independent variable be in this study?

**1-b)** What would the dependent variable be in this study?

**Question 2 (a-d)**

Hsee and Tang (2007) reported the results of a study in which 195 college students completed a happiness scale (from 1 to 7) one day in class. On this scale, 1 corresponded to very unhappy and 7 to very happy. On average, the students rated their happiness as 6.18. Identify each of the following for this study. PSYC 354 Homework 1 – Introduction to Statistics Assignments

**Questions 3-6**

Answer these general SPSS questions.

**3)** In which window do you enter data in SPSS?

**4)** Which window displays the results of your analysis in SPSS?

**5)** Which SPSS main menu would you use to choose a particular statistical test?

**6)** If you wanted to custom define a variable in SPSS, which window would you open?

**Question 7**

Suppose you have administered a personality inventory to 12 people and have recorded their score on each item in SPSS. The personality inventory has 8 items, so the SPSS file has 8 variables representing each item (item1, item2, etc.). You want to compute a total score for each participant that represents the sum of items 1–8.

**7a)** Which main SPSS menu contains the option for computing a variable like this?

**7b)** According to the presentation and to Lesson 19 in Green and Salkind, what could you type into the “Numeric Expression” text box in order to have SPSS add items 1–8 together? (There is more than one way to do this.)

Submit Homework 1 by 11:59 p.m. (ET) on Monday of Module/Week 1. Remember to name file appropriately.

**PSYC 354 Homework 2 Frequency Tables and Graphs**

All Questions

Part I: Concepts

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

Use the following table to answer Question 1. This table depicts the scores of 83 students on an exam worth 65 points.

**1)** Use the information in the table to determine the percentages for each interval. Depending on your rounding decisions, these may or may not add up to exactly 100% but should be very close.

Table: Grouped Frequency Table

Exam score Frequency

60–62 3

57–59 9

54–56 21

51–53 18

48–50 14

45–47 10

42–44 8

TOTAL 83

**2)** When constructing a histogram and labeling the x- and y-axes, the lowest number on each axis should ideally be ……

**3)** A frequency distribution that is bell-shaped, symmetrical, and unimodal is

**4)** A frequency distribution that has a tail trailing off to the right of the distribution is

**5)** A frequency distribution of ages of residents at a senior citizen home is clustered around 83 with a long tail to the left. This distribution is

**6)** When a variable cannot take on values above a certain level, this is known as a(n) effect.

**7)** A grouped frequency table has the following intervals: 30–44, 45–59, and 60–74. If converted into a histogram, what would the midpoints be?

**8)** Do the data below show a linear relation, non-linear relation, or no relation at all?

**9)** Do the data below show a linear relation, non-linear relation, or no relation at all? PSYC 354 Homework 1 – Introduction to Statistics Assignments.

**Part I:**

**Question 10a- 10e**

• Read the introduction and click on different “subway lines” to see how the interactive graph works.

**10-a)** In which of the four boroughs is the median household income highest?

**10-b)** Click on the “A” line. Does the line graph for Manhattan show high or low variability? What does this level of variability tell us about the household income in this area of Manhattan?

**10-c)** Click on line 2. Which borough (not a street) shows the least variability in median household income?

**10-d)** On line 2, find the following two subway stops: Park Place (the first of the highest Manhattan stops) and E 180 St. (one of the lowest Bronx stops, located about halfway across the BRX section). What is the difference (calculate) between the median household incomes of the two areas?

**10-e)** Click on the “D” line. Which subway stop in Brooklyn seems to be an outlier?

**Part II: SPSS Analysis**

Green and Salkind, Lesson 20

• Open the “Lesson 20 Exercise File 1” document (found in the course’s Assignment Instructions folder) in order to complete these exercises.

• Always use the Blackboard files instead of the files on the Green and Salkind website as some files have been modified for the purposes of this course.

• Reminder: For Exercise 1, be sure to paste in the SPSS output and write out the answers for A, B, and C beneath it.

**Part III: SPSS Data Entry and Analysis**

The steps will be the same in Part III as the ones you have been practicing in Part I of the assignment; the only difference is that you are now responsible for creating the data file as well. Remember to do the following:

• Name and define your variables under the “Variable View,” then return to the “Data View” to enter the data; and

• Paste all SPSS output and graphs into your homework file at the appropriate place. PSYC 354 Homework 1 – Introduction to Statistics Assignments.

**Part III: Questions 1a-1c**

**PSYC 354 Homework 3 Central Tendency and Variability**

Questions 1–7

Questions 1-4

Fill in the highlighted blanks to answer/complete the statements.

The arithmetic average of a set of numbers is the mean.

2) What is an outlier?

3) Which widely-used measure describes the typical amount or distance a score deviates from the mean in any given distribution?

3. Standard Deviation (-2) – correction from professor

4) What is the mathematical relationship between variance and standard deviation?

**Part I: Concepts**

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

**Question 5**

For the following terms, write the equivalent mathematical symbol (letter or letters) for the sample statistic.

Question 6a-6c

These are the winning percentages for 11 baseball players for each one’s best 4-year pitching performance:

6-c ) Compare the mean and median. Does the difference between them suggest that the data are skewed very much?

6-a) What is the mean of the scores? (Compute this using a calculator):

6-b) What is the median of these scores?

Explain.

**Question 7**

Recall the interactive graph from Homework 2 depicting household income and location in New

York City.

Based on this module/week’s reading, why do you think the author of this graph chose the median household income instead of the mean household income to describe central tendency?

**Part II: SPSS Analysis**

Green and Salkind Course Text, Lesson 21: Exercises 1, 4, 7, and 8

• Questions 1 and 4

o Green and Salkind Text, Lesson 21

o Lesson 21 Exercise File 1 (located under course’s Assignment Instructions folder)

**Part II:**

Exercises 1a-1d and Exercise 4

Green and Salkind, Lesson 21, Exercises 1 and 4

Open “Lesson 21 Exercise File 1” in order to complete these exercises.

**Part III: SPSS Data Entry and Analysis**

The steps will be the same as the ones you have been practicing in Part I of the assignment; the only difference is that you are now responsible for creating the data file, as well. Remember to do the following:

a) Name and define your variables under the Variable View, then return to the Data View to enter the data; and

b) Paste all SPSS output and graphs into your homework file at the appropriate place.

**Part III: Questions 1-4**

The following data are taken from the Bureau of Labor Statistics surveys from the years 2009–2013. They represent the average weekly pay for wage and salary earners measured at 4 different quarters each year and broken down by gender.

**PSYC 354 Homework 4**

Sampling and Probability

When submitting this file, be sure the filename includes your full name, course and section. Example: HW4_JohnDoe_354B01

Be sure you have reviewed this module/week’s lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file.

**Questions 1–15**

**Part I: Concepts**

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

**Questions 1-10**

Fill in the highlighted blanks to answer/complete the statements.

**1)** A (n) random sample occurs when everyone in the population has the same chance of being selected.

**2)** The ability to apply research findings to contexts or samples other than the one studied is called generalizability.

**3)** The duplication of the results of a research study in a different context or with a different sample is called replication. PSYC 354 Homework 1 – Introduction to Statistics Assignments.

**4)** Your own estimate of the likelihood that you will uphold your New Year’s resolution is known as a(n) personal probability.

**5)** Expected relative-frequency probability is computed as the number of successes divided by the number of trials.

**6)** The experimental group is the group receiving the intervention or treatment of interest.

**7)** A statement that 2 populations are different from one another is a(n) research hypothesis.

**8)** If you find that the groups you studied differed from each other more than would be expected by chance alone, you reject the null hypothesis.

**9)** When you reject the null hypothesis but the null hypothesis is in fact true, you have made a(n) Type I error.

**10)** When you fail to reject the null hypothesis but the null hypothesis is false, you have made a(n) Type II error.

**Question 11**

Researchers were interested in whether touch therapy improves the weight gain of preterm infants and compared the weight gain over a 3-week period of infants receiving touch therapy to the weight gain of infants not receiving touch therapy.

**11-a)** What is the likely null hypothesis for this experiment?

Touch therapy does not improve the weight gain of preterm infants.

**11-b)** What is the likely research hypothesis for this experiment?

Touch therapy does improve the weight gain of preterm infants.

**Question 12-15**

Complete the Nolan and Heinzen end-of-chapter Exercises 5.26, 5.27, 5.28, and 5.29.

**12)** Exercises 5.26

71/489=0.1452

**13)** Exercises 5.27

8/266=0.0301

**14)** Exercises 5.28

a) 1.73%

b) 80%

c) 37.19%

**15)** Exercises 5.29

a) 0.627

b) 0.003

c) 0.042

**Part II & Part III**

There is no new SPSS material this module/week. No questions for Part II or III

**Part IV: Cumulative**

Data provided below for Questions 1 and 2.

Grade Part IV: Questions 1a-1b

The final grades for students in a freshman seminar are shown in the left-hand column. Enter the data into a new SPSS data file.

• Create the appropriate SPSS graph to show the distribution of students’ grades.

• Compute descriptive statistics for this data.

• Which measure of central tendency would you use to describe this data?

• Why?

99.00

93.00

89.00

86.00

82.00

79.00

78.00

76.00

75.00

75.00

73.00

72.00

69.00

65.00

63.00

55.00

50.00

**1-a)** Create the appropriate SPSS graph to show the distribution of students’ grades.

Page 3 of 6

Answer:

**1-b)** Compute descriptive statistics for this data.

Which measure of central tendency would you use to describe this data? Why?

Page 4 of 6

Answer:

Descriptives

Statistic

Std. Error

Mean

95% Confidence Interval for Lower Bound

Mean Upper Bound

5% Trimmed Mean

Median

Variance

Grade Std. Deviation Minimum Maximum Range

Interquartile Range

Skewness

Kurtosis

75.24

3.097

68.67

81.80

75.32

75.00

163.066

12.770

50

99

49

17

-.146

.550

.037

1.063

Answer: Measure Of Central Tendency

Mean

Explanation/Justification:

You generally use the mean unless there are outliers or a small amount of observations. Neither is the case for this. Also, the mean and median are only 0.24 points different and the mode is the same as the median.

Page 5 of 6

Answer:

Explanation/Justification: You would use a bar graph because the independent variable is nominal and the dependent variable is scale.

**2-b)** What level of measurement (nom., ord., scale) is the variable “City”?

What level of measurement is the variable “Livability Rating”?

Nominal

Scale 2.b. ratings are ordinal (-2) – correction from professor

Submit Homework 4 by 11:59 p.m. (ET) on Monday of Module/Week 4. Remember to name file appropriately.

**PSYC 354 Homework 5**

**Z-Scores**

**Questions 1–9**

**Part I: Concepts**

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

What are always the mean and standard deviation of the z-distribution? (2 pts)

**2)** Define the central limit theorem. (1 pt)

**3) **Fill in the blanks (1 pt): A z-score is based on a distribution of equally likely events, while a z- statistic is based on a distribution of sample percentage or average.

**Part I: Questions 4-8**

Module 5 Lesson 21 Exercise File 1

**Part II: SPSS Analysis**

Open the “Lesson 21 Exercise File 1” document (found in the course’s Assignment Instructions folder) in order to complete these exercises.

**PSYC 354 Homework 6 Percentiles and Hypothesis Testing with Z-Tests**

**Questions 1–4**

**Part I: Concepts**

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

**Part I: Questions 1-8**

End-of-chapter problems:

Exercise 7.8 (1 pt)

**2)** Exercise 7.18 (1 pt each)

**3)** Exercise 7.20 (1 pt each)

More Questions Included

**PSYC 354 Homework 7**

Confidence Intervals, Effect Size, and Statistical Power

**Part I: Concepts**

**Questions 1–8**

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

**Part I: Questions 1a-1e**

Fill in the highlighted blanks with the best word or words.

**Part I: Questions 2-5**

End-of-chapter problems:

Complete the following Nolan and Heinzen end-of-chapter exercises for Chapter 8: 8.15, 8.22, 8.26, and 8.40.

If applicable, remember to show work in your homework document to receive partial credit.

More Questions Included

**PSYC 354 Homework 8**

**Single-Sample T-Test**

When submitting this file, be sure the filename includes your full name, course and section. Example:

Be sure you have reviewed this module/week’s lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file.

**Part I: Concepts**

**Questions 1–3**

These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.

**Part I: Questions 1a-1g**

Fill in the highlighted blanks with the best word or words.

**Part II: SPSS Analysis**

**Module/Week 8 Exercise File 1**

Open the “Module/Week 8 Exercise File 1” document (found in the course’s Assignment Instructions folder) in order to complete these exercises.

**Part II:**

**Exercises 1-3**

Use file: Module/Week 8 Exercise File 1

End-of-chapter exercise 9.37 in Nolan and Heinzen text

**Part III: SPSS Data Entry and Analysis**

Data provided below.

**Part IV: Cumulative**

Data provided below for respective questions.

**PSYC 354 Review Test Exam 4**

Attempt Score 97.5 points scored

**Instructions**

Time limit: 1 hour and 30 minutes

40 multiple-choice questions

Open¬book/open¬notes

Results Displayed Submitted Answers

**Question 1**

Imagine that the confidence interval around a group’s mean is [980, 1160], what is the mean?

**Question 2**

A negatively skewed distribution would most likely violate which assumption?

**Question 3**

A researcher conducts a single¬sample t test and finds statistical significance at the 0.01 level.

**Question 4**

The formula “ ” is used to represent the:

**Question 5**

Cohen’s d is one measure of:

**Question 6**

The single¬sample t test compares a sample mean to a population mean when:

**Question 7**

do we use to compare a sample to the population?

**Question 8**

Why are effect sizes rather than test statistics used when comparing study results?

**Question 9**

What falls within the 95% confidence interval?

**Question 10**

We calculate a statistical power and find that it is 0.93. This means that if the null hypothesis is , we have a % chance of rejecting the null hypothesis.

**Question 11**

A confidence interval is a(n. that includes the population mean after repeatedly sampling.

**Question 12**

One of the roles of the researcher performing a meta¬analysis is to:

**Question 13**

The statement “The findings based on a sample of 1000 participants were statistically significant, providing evidence for our hypothesis” would be strengthened by:

**Question 14**

We can increase statistical power with each of the following except:

**Question 15**

Imagine that a study of memory and aging finds that younger participants correctly recall 55% of studied words, older participants correctly recall 42% of studied words, and the size of this effect is Cohen’s d = 0.49. This effect size indicates that the memory performance of:

**Question 16**

That a results is statistically significant does not mean that it is

**Question 17**

When we report that something is statistically significant, it means that

**Question 18**

Increasing sample size:

**Question 19**

Many companies that manufacture light bulbs advertise their 60¬watt bulbs as having an average life of 1000 hours. A cynical consumer bought 30 bulbs and burned them until they failed. He found that they burned for an average of M = 1233, with a standard deviation of s =

232.06. What statistical test would this consumer use to determine whether the average burn time of light bulbs differs significantly from that advertised?

**Question 20**

The correct formula for effect size using Cohen’s d for a single¬sample t test is:

**Question 21**

In statistics, what does “homogeneous” mean?

**Question 22**

According to Cohen’s convention, a value of is a small effect size.

**Question 23**

Meta¬analysis involves:

**Question 24**

The practical use of statistical power is that it informs you the researcher:

**Question 25**

Alpha refers to:

**Question 26**

The larger the effect size, the:

**Question 27**

Candidate #2 received 32% of the votes and candidate #3 received 14% of the votes, with a margin of error of 6%. What does this information tell us about the popularity of these candidates?

**Question 28**

Statistical convention for the minimal acceptable power is:

**Question 29**

The numerator (top portion) of the ratio for calculating all the t statistics contains:

**Question 30**

Identify the formula for the single¬sample t test. PSYC 354 Homework 1 – Introduction to Statistics Assignments

**Question 31**

The second step in conducting the single¬sample t test involves

**Question 32**

Which of the following reports of statistical results are in appropriate APA format?

**Question 33**

According to Cohen’s convention, a value of is a large effect size.

**Question 34**

Effect size assesses the degree to which two:

**Question 35**

The formula for the degrees of freedom for the single¬sample t test is:

**Question 36**

Using the following information, convert the z score to a raw score: z = ¬2.3, mu = 15.5, sigma = 4.

**Question 37**

In a distribution of Z scores, the mean is always

**Question 38**

A population is normally distributed with ? = 30, ? = 10, and our sample N = 25. What are the mean and standard error of the distribution of

**Question 39**

A population is normally distributed with ? = 50, ? =

**Question 40**

If the mean of a test is 13 and its standard deviation is 3, the Z score for a person with a raw score of 7 is