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fundamentals of statistics
Questions and Answers of
Fundamentals Of Statistics
In the ambulance response time example (Exercise 8), a \(95 \%\) confidence interval with a width of approximately \(31 / 4\) minutes was constructed based on a sample of 67 runs \((N=67)\). Using
Calculate the \(90 \%\) confidence interval for the first three situations in Exercise 1 (a-d).
Calculate the \(99 \%\) confidence interval for the first three situations in Exercise 1 (a-d).
Calculate the \(90 \%\) and \(99 \%\) confidence interval for the Chips Ahoy example (Exercise 6).
Calculate the \(90 \%\) and \(99 \%\) confidence interval for the ambulance response time example (Exercise 8 ).
A pediatrician wanted to estimate the average temperature of children who come to her for treatment. She records the temperature of 23 children and calculates a mean of \(98.83^{\circ}\) and a
What changes to this book’s notational system are introduced as a function of having two groups rather than one?
What are the differences between visual displays of variables such as bar charts and visual displays of descriptive statistics such as bar graphs?
What is the main purpose and characteristics of the sampling distribution of the difference?
What is the difference between the sampling distribution of the mean (Chapter 7) and the sampling distribution of the difference?
What is the difference between the standard error of the mean (Chapter 7) and the standard error of the difference?
Construct a bar graph for each of the following situations (assume the independent variable is Gender and the dependent variable is Score):a. Males (N = 6, M = 3.00, s = 1.79); Females (N = 6, M =
For each of the following situations, (a) calculate the mean, standard deviation, and standard error of the mean for each group and (b) construct a bar graph (assume the independent variable is Type
In testing the difference between two sample means, what conclusions are represented by the null and alternative hypotheses (H0 and H1)?
What is the difference between the degrees of freedom (df) for the test of one sample mean and the difference between two sample means?
What are the main differences between the formulas for the t-test for one sample mean and the t-test for independent means?
What is the main difference between the formulas for the standard error of the mean and the standard error of the difference?
State the null and alternative hypotheses (H0 and H1) for the following research questions:a. Do children from single-parent families have higher self-esteem than children from intact families?b.
For each of the following situations, calculate the degrees of freedom (df) and identify the critical value of t (assume α = .05). a. N =7, N27, H1: H1* H2 = b. N 11, N2 C. 11. H: c. N 8, N28, H: H2
For each of the following situations, calculate the standard error of the difference (sX̅1 - X̅2). a. N =9, s 3.00, N = 9, 52 = 6.00 b. N = 16, s = 8.00, N = 16, 52 = 12.00 c. N = 24,5 = 3.38, N =
For each of the following situations, calculate the standard error of the difference (sX̅1 - X̅2) and the t-test for independent means. a. N = 6, X = 9.00, s = 3.00, N = 6, X = 6.00, 52 = 2.00 b. N
What are the two mathematical assumptions related to the t-test for independent means?
What does it mean to violate the assumption of heterogeneity of variance?
What does it mean for a statistic to be robust?
What can researchers do when they believe assumptions have been violated?
How much do you think the average adult woman weighs? Let’s imagine that a researcher, in response to available evidence from both the media and society, entertains the assumption that men believe
How does the calculation of the t-test for the difference between two sample means change when the sample sizes of the two groups are unequal?
For each of the following situations, calculate the standard error of the difference (sX̅1 - X̅2) using the formula for unequal sample sizes. a. N = 4, 5 = 2.00, N = 5, 52 = 3.00 b. N 20, s 6.00,
To assist parents whose children have been diagnosed as having the eating disorder anorexia nervosa, one study evaluated the impact of a program designed to provide parents access to information and
What is the main difference between between-subjects and within-subjects research designs?
For what types of research situations might you use a within-subjects design?
In analyzing a pretest-posttest research design, why do we calculate the difference between the scores in the two groups?
When would you calculate the t-test for dependent means rather than the t-test for independent means?
You conduct a class project in which you divide classmates into seven pairs; each pair consists of a shy student and an outgoing student. You have each pair of students work on a puzzle but do not
For each of the following situations, calculate the standard error of the difference scores (sD̅) and the t-test for dependent means. a. N = 9. XD = 2.00, s = 1.75 b. No 12,X=1.50, s = 3.50 c. N =
As adults get older, their lives may become increasingly sedentary. Given concerns about physical and psychological problems associated with a lack of physical activity, one study investigated
For each of the following, calculate the degrees of freedom ( \(d f\) ) and determine the critical values of \(t\) (assume \(\alpha=.05\) ).a. \(N_{1}=21, N_{2}=21, \mathrm{H}_{1}: \mu_{1} eq
For each of the following, calculate the degrees of freedom ( \(d f\) ) and determine the critical values of \(t\) (assume \(\alpha=.05\) ).a. \(N_{1}=5, N_{2}=5, \mathrm{H}_{1}: \mu_{1} eq
For each of the following, calculate the standard error of the difference \(\left(s_{\bar{X}_{1}-\bar{X}_{2}}\right)\).a. \(N_{1}=35, s_{1}=1.50, N_{2}=35, s_{2}=3.25\)b. \(N_{1}=4, s_{1}=4.30,
For each of the following, calculate the standard error of the difference \(\left(s_{\bar{X}_{1}-\bar{X}_{2}}\right)\).a. \(N_{1}=10, s_{1}=2.00, N_{2}=10, s_{2}=3.00\)b. \(N_{1}=19, s_{1}=1.73,
For each of the following, calculate the \(t\)-test for independent means.a. \(\bar{X}_{1}=3.49, \bar{X}_{2}=3.14, s_{\bar{X}_{1}-\bar{X}_{2}}=.31\)b. \(\bar{X}_{1}=13.27, \bar{X}_{2}=16.45,
For each of the following, calculate the \(t\)-test for independent means.a. \(\bar{X}_{1}=7.00, \bar{X}_{2}=11.00, s \bar{X}_{1}-\bar{X}_{2}=1.17\)b. \(\bar{X}_{1}=65.56, \bar{X}_{2}=60.92,
For each of the following, calculate the standard error of the difference \(\left(s_{\bar{X}_{1}}-\bar{X}_{2}\right)\) and the \(t\)-test for independent means.a. \(N_{1}=6, \bar{X}_{1}=18.50,
For each of the following, calculate the standard error of the difference \(\left(s_{\bar{X}_{1}-\bar{X}_{2}}\right)\) and the \(t\)-test for independent means.a. \(\quad N_{1}=11, \bar{X}_{1}=12.00,
When you're interviewing for a job, is your behavior influenced by beliefs the interviewer has about you? Researchers Ridge and Reber (2002) observed the interactions of 54 men, each of whom was
An advertising agency is interested in learning how to fit its commercials to the interests and needs of the viewing audience. It asked samples of 41 men and 41 women to report the average amount of
A pair of researchers was interested in studying men's preferences for a potential mate and how these preferences may change as men get older (Alterovitz \& Mendelsohn, 2009). The researchers
A third-grade teacher is interested in comparing the effectiveness of two styles of instruction in language comprehension: imagery, in which the students are asked to picture a situation involving
Imagine you believe that men and women have different beliefs regarding the average cost of a wedding. More specifically, because they are traditionally more involved in the planning of weddings and
For each of the following, calculate the standard error of the difference \(\left(s_{\bar{X}_{1}}-\bar{X}_{2}\right)\) (be sure to use the formula for unequal sample sizes).a. \(N_{1}=8, s_{1}=2.30,
For each of the following, calculate the standard error of the difference \(\left(s_{\bar{X}_{1}}-\bar{X}_{2}\right)\) (be sure to use the formula for unequal sample sizes).a. \(N_{1}=9, s_{1}=4.00,
A team of researchers stated that effective methods of therapy help people access and process their emotions (Watson \& Bedard, 2006). They looked at the level of emotional processing brought about
A team of audiologists was interested in examining whether their patients' satisfaction with their hearing aids was related to how long they had used hearing aids (Williams, Johnson, \& Danhauer,
Imagine a researcher asks a sample of five people to drive two types of cars and rate each of them on a 1 to 20 scale. Listed below are the data she collected:a. Calculate the difference score
For each of the following, calculate the standard error of the difference scores \(\left(s_{\bar{D}}\right)\) and the \(t\)-test for dependent means.a. \(N_{D}=25, \bar{X}_{D}=10.00,
For each of the following, calculate the standard error of the difference scores \(\left(s_{\bar{D}}\right)\) and the \(t\)-test for dependent means.a. \(N_{D}=10, \bar{X}_{D}=12.00,
As people in our society live longer, there is a growing need for older adults to maintain a healthy lifestyle, part of which is their physical fitness. One study evaluated a program designed to
Another part of the study discussed in Exercise 25 had a second sample of nine older adults take part in an 8 -week calisthenics program in which they did squats, hamstring curls, and lunges. As the
A group of friends decided to work together to decrease their cigarette smoking. They hypothesize that they can decrease their level of smoking by doing such things as giving one another
A researcher hypothesizes that an afternoon dose of caffeine lessens the amount of time a person sleeps at night. The participants are instructed to report their average hours of sleep per night for
For each of the following situations, calculate the population standard error of the mean (σX̅). a. = 18; N=36 b. 9.42; N=49 c. = 1.87; N=60 d. .91; N=22 21.43; N=106
For each of the following situations, calculate the z-statistic (z). a. X=14.00; =11; = 6; N = 36 b. X=7.00; 8; = 3; N = 9 C. X = 2.86; = 2.69; = .40; N = 29 d. X=10.12;u= 7.98; = 4.59; N = 26
For each of the following situations, calculate the z-statistic (z). a. X=8.00; =5; = 6; N = 16 b. X 4.00; = 2; = 8; N = 25 C. X=11.50; = 9.25; = 5.75; N = 38 d. X=.95;u= .82; = .31; N = 15 e.
For each of the following situations, calculate the population standard error of the mean (σX̅) and the z-statistic (z), make a decision about the null hypothesis, and indicate the level of
In the GRE test example (Exercise 9), what if it was believed that the only possible alternative to the null hypothesis is one in which the students’ GRE scores increase (i.e., they cannot
For each of the following situations, calculate the degrees of freedom (df ) and determine the critical values of t. a. N=10; = .05; H: 5 b. N=20; = .05; H: 5 c. N=10; = .01; H: 5 d. N=20; = .01;
For each of the following situations, calculate the standard error of the mean (sX̅). a. S=7.00; N=49 b. s 2.50; N=14 c. s=8.90; N=23 d. s 25.61; N=54
For each of the following situations, calculate the standard error of the mean (SX̅). a. s=5.00; N=16 b. 17.82; N = 10 c. s 2.31; N = 37 = d. s=51.32; N=21
For each of the following situations, calculate the t-statistic (t): a. X=12.00; =10; x = 2.00 b. X=6.00; =9; sx=1.50 C. X=4.25;u=4.25; x=.75 d. =5.62;u=5.25; x=.20 e. X=9.75;u=10.50; x=1.08
For each of the following situations, calculate the t-statistic (t): a. X=11.00; =5; s=3.00 b. X=26.00;u=31; s=2.00 c. X=19.60;u= 22; $x = 3.25 d. X=3.27;u=3; 5x=.13 e. X=74.92; u 65.50; s=5.16
For each of the following situations, calculate the t-statistic (t): a. X=4.00;u=5; s=3.00; N = 36 b. X=1.50;u=1.25; s= .75; N = 25 C. X=16.21;u=15; s=3.23; N = 46 d. X=8.26;u=6.31; s=3.71; N = 12 e.
For each of the following situations, calculate the t-statistic (t): a. X= .45; u .52; s=.17; N=56 b. X=7.75;u= 6; s= 3.98; N = 40 C. X=3.31;u=4; s=1.33; N = 35 d. X=37.83;u=40.95; s= 7.74; N=21 e.
For each of the following situations, calculate the t-statistic (t): a. X=20.00;u=18; s=1.00 b. X=20.00;u=13;x=1.00 C. X=12.00; = 20; x=1.00 d. Looking at your answers to (a-c), how is the
For each set of data below, calculate the sample size (N), the mean (X̅), the standard deviation (s), the standard error of the mean (SX̅), and the t-statistic (t). Note: assume μ = 12.a. 9, 14,
For each of the following situations, draw a normal distribution (a.k.a. “bell-shaped curve”), mark the critical value(s), shade in the region of rejection, compare the stated t-statistic to the
The manager of a department store disputes the company’s claim that the average age of customers who buy a particular brand of clothes is 16; she believes the average age is older than 16. A clerk
In the department store example, imagine that the sample had been N = 4 rather than N = 25 (for the sake of this example, keep the sample mean and standard deviation at 18.50 and 2.25,
One of the examples in this chapter discussed unique invulnerability, the belief that people will provide estimates of age at time of death that are greater than the average life expectancy in the
The American Statistical Association publishes a monthly magazine sent to all of its members. This magazine once included an article that asked, “How many chocolate chips are there in a bag of
A sixth-grade teacher uses a new method of teaching mathematics to her students, one she believes will increase their level of mathematical ability. To assess their mathematical ability, she
For each of the sets of data in Exercise 5, calculate the variance (σ2) using the definitional formula and the computational formula.
For each of the sets of data in Exercise 5, calculate the population variance (σ2) using the definitional formula.Comparing your calculations for each data set with those done in Exercise 7, which
For each of the sets of data in Exercise 5, calculate the standard deviation (s) and the population standard deviation(σ). For each data set, which is larger, the standard deviation or the
A friend of yours asks 20 people to rate a movie using a 1- to 5-star rating: the higher the number of stars, the higher the recommendation. Their ratings are listed below:a. Calculate the variance
One study stated the research hypothesis, “Violence behavior in children may be reduced by teaching them conflict resolution skills” (DuRant et al., 1996). The variable “violence behavior”
The 10% myth study discussed in this chapter measured the beliefs of both psychology majors and non–psychology majors. The 39 non–psychology majors in this study provided the following values for
An instructor administers a 27-item quiz to her class of 25 students. Each student's score on the quiz is the number of items answered correctly. These scores are listed below:a. Calculate the
On your own, create two distributions of 10 scores that have the same mean but differ in modality: one unimodal and one bimodal. Calculate the standard deviation of the two distributions. Is there
On your own, (a) create two distributions of 10 scores that have the same mean but differ in their amount of variability, and (b) create two distributions of 10 scores that have different means but
What if someone told you, “There is very little variability in the scores for my variable.” From this statement, would you be more likely to describe the shape of the distribution as peaked or
What if someone told you, “There is a great deal of variability in the scores for my variable.” From this statement, can you tell whether the shape of the distribution is symmetrical or skewed?
What if someone told you, “The mean age of the participants in this sample was 35.50 and the standard deviation was 2.53.” Why would you interpret the sample differently if you had been told the
An employment survey in 2009 was conducted to find the average starting salaries of people receiving doctorate(PhD) degrees in psychology (Michalski, Kohout, Wicherski, & Hart, 2011). The mean
What are the main features and characteristics of normal distributions?
Why are normal distributions important to researchers?
What is a problem or concern about using normal distributions?
What are the main features of the standard normal distribution?
What distinguishes the standard normal distribution from normal distributions?
What are the characteristics of z-scores?
What are the two main ways z-scores may be interpreted?
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