Scores on a standardized reading test for fourth-grade students form a normal distribution with μ = 71 and σ = 24. What is the probability of obtaining a sample mean greater than M = 63 for each of the following? a. A sample of n = 9 students b. A sample of n = 36 students c. A sample of n = 64 students
> A researcher reports an F-ratio with df = 4, 62 from an independent-measures research study. a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study? c. Use Appendix B to find the critical va
> A local fast-food restaurant normally sells coffee in three sizes—small, medium, and large—at three different prices. Recently they had a special sale, charging only $1 for any sized coffee. During the sale, an employe
> A sample of n = 12 individuals participates in a repeated-measures study that produces a sample mean difference of MD = 7.25 with SS = 396 for the difference scores. a. Calculate the standard deviation for the sample of difference scores. Briefly explain
> A researcher conducts an experiment comparing two treatment conditions with 22 scores in each treatment condition. a. If an independent-measures design is used, how many subjects are needed for the experiment? b. If a repeated-measures design is used, ho
> What is the defining characteristic of a repeated-measures or within-subjects research design?
> For the each of the following studies determine whether a repeated-measures t test is the appropriate analysis. Explain your answers. a. A researcher is examining the effect of violent video games on behavior by comparing aggressive behaviors for one gro
> Two separate samples, each with n = 9 individuals, receive different treatments. After treatment, the first sample has SS = 546 and the second has SS = 606. a. Find the pooled variance for the two samples. b. Compute the estimated standard error for the
> One sample has SS = 72 and a second sample has SS = 24. a. If n = 7 for both samples, find each of the sample variances and compute the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway be
> For each of the following, assume that the two samples are obtained from populations with the same mean, and calculate how much difference should be expected, on average, between the two sample means. a. Each sample has n = 7 scores with s2 = 142 for the
> Two samples are selected from the same population. For each of the following, calculate how much difference is expected, on average, between the two sample means. a. One sample has n = 6, the second has n = 10, and the pooled variance is 135. b. One samp
> As noted on page 332, when the two population means are equal, the estimated standard error for the independent- measures t test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume th
> Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic.
> A research study comparing alcohol use for college students in the United States and Canada reports that more Canadian students drink but American students drink more (Kuo, Adlaf, Lee, Gliksman, Demers, & Wechsler, 2002). Is this study an example of an e
> Describe the homogeneity of variance assumption and explain why it is important for the independent measures t test.
> Describe the basic characteristics that define an independent-measures, or a between-subjects, research study.
> Find the t values that form the boundaries of the critical region for a two-tailed test with α = .05 for each of the following sample sizes: a. n = 6 b. n = 12 c. n = 48 d. Repeat parts a–c assuming a one-tailed test, α = .05. e. Repeat parts a–c assumin
> Explain why t distributions tend to be flatter and more spread out than the normal distribution.
> The following sample of n = 7 scores was obtained from a population with unknown parameters. Scores: 2, 18, 15, 5, 15, 8, 7. a. Compute the sample mean and variance. (Note: These are descriptive values that summarize the sample data.) b. Compute the esti
> Find the estimated standard error for the sample mean for each of the following samples. a. n = 9 with SS = 1,152 b. n = 16 with SS = 540 c. n = 25 with SS = 600
> A sample of n = 25 scores has a mean of M = 200 and a variance of s2 = 100. a. Explain what is measured by the sample variance. b. Compute the estimated standard error for the sample mean and explain what is measured by the standard error.
> Suppose that a researcher is interested in whether an exercise improves intelligence. The researcher randomly selects 100 participants, assigns them to an exercise program, and measures intelligence at the end of the exercise program. The measurement of
> Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?
> Explain how each of the following influences the value of the z-score in a hypothesis test. a. Increasing the size of the treatment effect. b. Increasing the population standard deviation. c. Increasing the number of scores in the sample.
> The international affective picture system is a collection of images that differ in their emotional content. The system contains some images that evoke fear in participants (e.g., a photograph of a spider), some images that have little emotional content
> If the alpha level is changed from α = .05 to α = .01: a. What happens to the boundaries for the critical region? b. What happens to the probability of a Type I error?
> Define the alpha level and the critical region for a hypothesis test.
> Suppose that a researcher is interested in the effect of a new college preparation course on scores for a standardized critical thinking test with a population mean of μ = 20. Students receive training in the course and later receive the standardized tes
> Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant. a. Increasing the alpha level from .01 to .05. b. Changing from a one-tailed test to a two-tailed test. c. Increasing effe
> Identify the four steps of a hypothesis test as presented in this chapter.
> Suppose that a treatment effect increases both the mean and the standard deviation of a measurement. Can a hypothesis test with z be conducted? Explain your answer.
> Does a hypothesis test allow a researcher to claim that an alternative hypothesis is true? Explain your answer.
> Suppose that a professor randomly assigns students to study groups of n = 4 students. The final exam in the professor’s class has a mean of μ = 75 and a standard deviation of σ = 10. What is the expected value of the mean and the standard deviation of th
> For a sample of n = 36 scores, what is the value of the population standard deviation (s) necessary to produce each of the following standard error values? a. σ M = 12 points b. σ M = 3 points c. σ M = 2 points
> A random sample is selected from a population with a standard deviation of σ = 18. a. On average, how much difference should there be between the sample mean and the population mean for a random sample of n = 4 scores from this population? b. On average,
> Gentile, Lynch, Linder, and Walsh (2004) surveyed more than 600 eighth- and ninth-grade students regarding their gaming habits and other behaviors. Their results showed that the adolescents who experienced more video game violence were also more hostile
> Under what circumstances is the distribution of sample means guaranteed to be a normal distribution?
> Describe the distribution of sample means (shape, mean, and standard error) for samples of n = 64 selected from a population with a mean of μ = 90 and a standard deviation of σ = 32.
> A sample is selected from a population with a mean of μ = 100 and a standard deviation of σ = 20. a. If the sample has n = 16 scores, what is the expected value of M and the standard error of M? b. If the sample has n = 100 scores, what is the expected v
> A sample of n = 36 scores is selected from a normal distribution with a mean of μ = 65. Compute the z-score for a sample mean of M = 59 and determine whether the sample mean is a typical, representative value or an extreme value for each of the following
> Metacognition is an understanding of one’s own cognitive processes, like thoughts, perceptions, and memory. In a recent study of metacognition in monkeys, a researcher presented monkeys with either a tube that was closed except at both
> If the population standard deviation is σ = 24, how large a sample is necessary to have a standard error that is a. equal to 6 points? b. equal to 3 points? c. equal to 2 points?
> For a population with σ = 16, how large a sample is necessary to have a standard error that is a. equal to 8 points? b. equal to 4 points? c. equal to 2 points?
> For a population with a mean of μ = 72 and a standard deviation of σ = 10, what is the standard error of the distribution of sample means for each of the following sample sizes? a. n = 4 scores b. n = 25 scores
> By definition, jumbo shrimp are those that require between 10 and 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages μ = 12.5 with a standard deviation of σ = 1.5, and forms a normal distribution. What is the pro
> Suppose that all possible n = 50 samples are selected from a population. How would the mean, standard deviation, and shape of the resulting sampling distribution compare to a sampling distribution based on all possible n = 100 samples?
> For the following set of scores: a. Organize the scores in a frequency distribution table. b. Based on the frequencies, identify the shape of the distribution.
> A population has a mean of μ = 30 and a standard deviation of σ = 8. a. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 4? b. If the population distribution is positivel
> A normal distribution has a mean of μ = 58 and a standard deviation of σ = 12. a. What is the probability of randomly selecting a score less than X = 52? b. What is the probability of selecting a sample of n = 9 scores with a mean less than M = 52? c. Wh
> Scores from a questionnaire measuring social anxiety form a normal distribution with a mean of μ = 50 and a standard deviation of σ = 10. What is the probability of obtaining a sample mean greater than M = 53 a. for a random sample of n = 4 people? b. fo
> A population forms a normal distribution with a mean of μ = 85 and a standard deviation of σ = 24. For each of the following samples, compute the z-score for the sample mean. a. M = 91 for n = 4 scores b. M = 91 for n = 9 scores c. M = 91 for n = 16 scor
> A sample of n = 64 scores has a mean of M = 68. Assuming that the population mean is μ = 60, find the z-score for this sample: a. If it was obtained from a population with σ = 16 b. If it was obtained from a population with σ = 32 c. If it was obtained f
> Sales representatives at a cellular phone retailer sell a mean of μ = 200 and a standard deviation of σ = 50 smartphones per year. At the Rochester, New York, branch, n = 25 representatives sell M = 220. Compute the z-score for the Rochester branch.
> For a population with a mean of μ = 40 and a standard deviation of σ = 12, find the z-score corresponding to each of the following samples. a. X = 52 for a sample of n = 1 score b. M = 52 for a sample of n = 9 scores c. M = 52 for a sample of n = 16 scor
> What proportion of a normal distribution is located between each of the following z-score boundaries? a. z = -1.64 and z = +1.64 b. z = -1.96 and z = +1.96 c. z = -1.00 and z = +1.00
> Find each of the following probabilities for a normal distribution. a. p(z > +2.00) b. p(z > -1.00) c. p(z < +0.50) d. p(z < +1.75)
> Describe how the goal of an experimental research study is different from the goal for nonexperimental or correlational research. Identify the two elements that are necessary for an experiment to achieve its goal.
> Draw a vertical line through a normal distribution for each of the following z-score locations. Find the proportion of the distribution located between the mean and the z-score. a. z = +1.60 b. z = +0.90 c. z = -1.50 d. z = -0.40
> Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the tail is on the right or left side of the line and find the proportion in the tail. a. z = +1.00 b. z = +0.33 c. z = -0.10 d. z = -0.67
> Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body. a. z = +2.00 b. z = +0.50 c. z = -1.50 d. z = -1.67
> Bags of Skittles™ candies include six different colors: red, orange, yellow, green, blue, and purple. If the bag has an equal number of each of the six colors, what are the probabilities for each of the following? a. Randomly selecting a green candy? b.
> A psychology class consists of 32 freshmen and 48 sophomores. If the professor selects names from the class list using random sampling, a. what is the probability that the first student selected will be a freshman? b. and if a random sample of n = 6 stud
> Suppose that a researcher is interested in the effect of new smart drug on IQ. Scores from the IQ test are normally distributed with a mean of μ = 100 and σ = 15. A participant receives the smart drug and completes the IQ assessment. a. If the treatment
> Seattle, Washington, averages μ = 34 inches of annual precipitation. Assuming that the distribution of precipitation amounts is approximately normal with a standard deviation of σ = 6.5 inches, determine whether each of the following represents a fairly
> According to a recent report, the average American consumes 22.7 teaspoons of sugar each day (Cohen, August 2013). Assuming that the distribution is approximately normal with a standard deviation of σ = 4.5, find each of the following values. a. What per
> Suppose that the distribution of scores on the Graduate Record Exam (GRE) is approximately normal, with a mean of μ = 150 and a standard deviation of σ = 5. For the population of students who have taken the GRE: a. What proportion have GRE scores less th
> For a normal distribution with a mean of m = 85 and a standard deviation of s = 20, find the proportion of the population corresponding to each of the following. a. Scores greater than 89 b. Scores less than 72 c. Scores between 70 and 100
> Describe the data for a correlational research study and explain how these data are different from the data obtained in experimental and nonexperimental studies, which also evaluate relationships between two variables.
> Find the z-score boundaries that separate a normal distribution as described in each of the following. a. The middle 95% from the 5% in the tails b. The middle 50% from the 50% in the tails c. The middle 75% from the 25% in the tails d. The middle 60% fr
> Find the z-score boundaries that separate a normal distribution as described in each of the following. a. The middle 20% from the 80% in the tails b. The middle 25% from the 75% in the tails c. The middle 70% from the 30% in the tails d. The middle 90% f
> Find the z-score location of a vertical line that separates a normal distribution as described in each of the following. a. 5% in the tail on the right b. 20% in the tail on the left c. 90% in the body on the right d. 50% on each side of the distribution
> Find each of the following probabilities for a normal distribution. a. p(-1.80 < z < 0.20) b. p(-0.40 < z < 1.40) c. p(0.25 < z < 1.25) d. p(-0.90 < z < -0.60)
> What are the two requirements for a random sample?
> A sample has a mean of M = 90 and a standard deviation of s = 20. a. Find the z-score for each of the following X values. b. Find the X value for each of the following z-scores.
> For a population with μ = 80 and σ = 9, find the z-score for each of the following X values.
> For a population with μ = 50 and σ = 6: a. Find the z-score for each of the following X values. b. Find the score (X value) that corresponds to each of the following z-scores.
> For a sample with a standard deviation of s = 15, describe the location of each of the following z-scores in terms of its position relative to the mean. For example, z = +1.00 is a location that is 15 points above the mean. a. z = -1.20 b. z = +0.80 c. z
> For a population with a standard deviation of σ = 10, find the z-score for each of the following locations in the distribution. a. Above the mean by 10 points b. Above the mean by 5 points c. Below the mean by 20 points d. Below the mean by 6 points
> The following scores are the ages for a random sample of n = 32 drivers who were issued parking tickets in Chicago during 2019. Determine the best interval width and place the scores in a grouped frequency distribution table. From looking at your table,
> A score of X = 75 is measured in a population with a mean of μ = 100. A z-score of z = +1.50 is calculated. Without knowing the standard deviation, explain why the z-score of z = +1.50 is incorrect.
> For each of the following populations, would a score of X = 85 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)? a. μ = 75 and σ = 15 b. μ = 80 and σ = 2 c. μ = 90 and σ = 2
> A researcher is interested in the effects of a “smart drug” on performance on a standardized intelligence test with a mean of μ = 200 and a standard deviation of σ = 50. Suppose that a participant who receives the smart drug subsequently earns a score of
> A sample consists of the following n = 5 scores: 8, 4, 10, 0, 3. a. Compute the mean and standard deviation for the sample. b. Find the z-score for each score in the sample. c. Transform the original sample into a new sample with a mean of M = 100 and s
> Identify the letters in the following distribution that correspond to the following z-scores. a. z = 12.00 b. z = 0.00 c. z = 22.00 d. z = 20.50
> A population consists of the following N = 7 scores: 6, 1, 0, 7, 4, 13, 4. a. Compute μ and σ for the population. b. Find the z-score for each score in the population. c. Transform the original population into a new population of N = 7 scores with a mean
> A sample with a mean of M = 62 and a standard deviation of σ = 5 is transformed into a standardized distribution with μ = 50 and s = 10. Find the new, standardized score for each of the following values from the original population. a. X = 61 b. X = 55 c
> Your professor tells you that all exam scores were transformed to z-scores for the midterm examination. Describe the mean and standard deviation of the resulting distribution of z-scores.
> The Graduate Record Exam is a standardized test taken by many graduating college seniors. GRE scores are often included in applications to masters or doctoral programs. Suppose that a psychology major received a score of X = 160 on the verbal section of
> In a population distribution, a score of X = 56 corresponds to z = -0.40 and a score of X = 70 corresponds to z = +1.00. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.)
> Describe the difference in appearance between a bar graph and a histogram and describe the circumstances in which each type of graph is used to represent sample data. How would the same variables be represented in a population?
> For a sample with a mean of M = 63, a score of X = 54 corresponds to z = 20.75. What is the sample standard deviation?
> For a sample with a standard deviation of s = 4, a score of X = 35 corresponds to z = -1.25. What is the sample mean?
> You are told that the results of an extraversion assessment gave you a z-score of +2.00. What does that mean about your level of extraversion relative to the mean?
> For a population with a mean of μ = 45, a score of X = 54 corresponds to z = +1.50. What is the population standard deviation?
> For a population with a standard deviation of σ = 12, a score of X = 115 corresponds to z = +1.25. What is the population mean?
> For a population with a standard deviation of σ = 4, a score of X = 24 corresponds to z = 21.50. What is the population mean?
> A score that is 10 points above the mean corresponds to a z-score of z = +1.20. What is the sample standard deviation?
> A score that is 20 points below the mean corresponds to a z-score of z = - 0.50. What is the population standard deviation?
> Find the z-score corresponding to X = 24 and the X value corresponding to z = +1.50 for each of the following samples. a. M = 20 and s = 12 b. M = 20 and s = 4 c. M = 30 and s = 8 d. M = 30 and s = 10
> Find the z-score corresponding to X = 105 and the X value corresponding to z = +0.40 for each of the following populations. a. μ = 100 and σ = 12 b. μ = 100 and σ = 4 c. μ = 80 and σ = 14 d. μ = 80 and σ = 6
> In your most recent checkup, your physician listed that your height is 70 inches, rounded to the nearest whole inch. Why is it unlikely that your height is exactly 70 inches? What are the upper and lower real limits of your height?
