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essentials of statistics
Essentials Of Statistics For The Behavioral Sciences 9th Edition Frederick J Gravetter, Larry B. Wallnau, Lori Ann B. Forzano - Solutions
Calculate the following from a frequency table: oX, oX2, and the proportion and percentage of the group associated with each score.
Choose when it is useful to set up a grouped frequency distribution table, and use and create this type of table for a set of scores.
Describe how the three types of frequency distribution graphs—histograms, polygons, and bar graphs—are constructed and identify when each is used.
Use and create frequency distribution graphs and explain how they are related to the original set of scores.
Explain how frequency distribution graphs for populations differ from the graphs used for samples.
Identify the shape of a distribution—symmetrical, and positively or negatively skewed—based on a set of scores or a frequency distribution graph.
If the following scores are placed in a frequency distribution table, then what is the frequency value corresponding to X 5 2? Scores: 2, 3, 1, 1, 3, 3, 2, 4, 3, 1a. 1b. 2c. 3d. 4
For the following distribution of quiz scores, how many individuals took the quiz?a. 5b. 10c. 15d. 21
For the following frequency distribution, what is the value of oX2?a. 50b. 55c. 74d. 225
A set of scores ranges from a high of X 5 96 to a low of X 5 27.If these scores are placed in a grouped frequency distribution table with an interval width of 10 points, the top interval in the table would be .a. 90–99b. 90–100c. 91–100d. 87–96
What is the lowest score in the following distribution?a. X 5 16b. X 5 17c. X 5 1d. cannot be determined
Which of the following statements is false regarding grouped frequency distribution tables?a. An interval width should be used that yields about 10 intervals.b. Intervals are listed in descending order, starting with the highest value at the top of the X column.c. The bottom score for each interval
Which of the following measuring scales are displayed by frequency distribution polygons?a. Either interval or ratio scalesb. Only ratio scalesc. Either nominal or ordinal scalesd. Only nominal scales
A group of quiz scores is shown in a histogram. If the bars in the histogram gradually decrease in height from left to right, what can you conclude about the set of quiz scores?a. There are more high scores than there are low scores.b. There are more low scores than there are high scores.c. The
Instead of showing the actual number of individuals in each category, a population frequency distribution graph usually shows a(n) .a. estimated frequencyb. grouped frequencyc. relative frequencyd. hypothetical frequency
In a distribution with positive skew, where are the scores with the highest frequencies located?a. On the right side of the distributionb. On the left side of the distributionc. In the middle of the distributiond. Represented at two distinct peaks
When constructing or working with a grouped frequency distribution table, a common mistake is to calculate the interval width by using the highest and lowest values that define each interval. For example, some students are tricked into thinking that an interval identified as 20–24 is only 4
Construct a frequency distribution table for the following set of scores. Include columns for proportion and percentage in your table.Scores: 4 5 7 8 1 6 8 7 4 4 6 3 4 7 6 4 5 3 5 5
Find each value requested for the distribution of scores in the following table.a. nb. oXc. oX2 X f 5 2 4 3 3 1 2 4 1 2
Find each value requested for the distribution of scores in the following table.a. nb. oXc. o(X 2 1)X f 10 1 9 2 8 4 7 3 6 2
For each of the following, determine the interval width that would be best for a grouped frequency distribution and identify the approximate number of intervals needed to cover the range of scores.a. Scores that range from X 5 6 to X 5 81b. Scores that range from X 5 18 to X 5 34c. Scores that
For the following scores, the smallest value is X 5 7 and the largest value is X 5 48.a. Determine the best interval width and identify the approximate number of intervals needed for a grouped frequency distribution table.b. Place the scores in a grouped frequency distribution table using the
The following scores are the ages for a random sample of n 5 32 drivers who were issued parking tickets in Chicago during 2015. Determine the best interval width and place the scores in a grouped frequency distribution table. From looking at your table, does it appear that tickets are issued
What information is available about the scores in a regular frequency distribution table that you cannot obtain for the scores in a grouped table?
For the following set of scores:7 5 4 4 6 5 2 3 2 4 5 8 5 8 3 3 6 4 7 3 4 3 3 6a. Construct a frequency distribution table to organize the scores.b. Draw a frequency distribution histogram for these data.
Draw a histogram for the distribution of scores shown in the following table.X f 10 2 9 4 8 1 7 1 6 4 5 2
Draw a polygon for the distribution of scores shown in the following table.X f 6 2 5 5 4 3 3 2 2 1
For the following set of scores:12 13 8 14 10 8 9 13 9 9 14 8 12 8 13 13 7 12a. Organize the scores in a frequency distribution table.b. Based on the frequencies, identify the shape of the distribution.
Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of the distribution?15 14 9 10 15 12 14 11 13 14 13 14 12 14 13 13 12 11
A survey given to a sample of college students contained questions about the following variables. For each variable, identify the kind of graph that should be used to display the distribution of scores (histogram, polygon, or bar graph).a. ageb. birth-order position among siblings (oldest 5
Gaucher, Friesen, and Kay (2011) found that words they identified as “masculine-themed” (such as competitive, independent, analyze, strong) are commonly used in job recruitment materials, especially for job advertisements in male-dominated areas. In a similar study, a researcher counted the
Find each of the following values for the distribution shown in the following polygon.a. nb. oXc. oX2 f7 65 43 21 123456 X
For the following set of scores:7 5 6 4 4 3 8 9 4 7 5 5 6 9 4 7 5 10 6 8 5 6 3 4 8 5a. Construct a frequency distribution table.b. Sketch a histogram showing the distribution.c. Describe the distribution using the following characteristics:(1) What is the shape of the distribution?(2) What score
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 employee recorded the number of each coffee size that was purchased on Wednesday
Weinstein, McDermott, and Roediger (2010) published an experimental study examining different techniques that students use to prepare for a test. Students read a passage, knowing that they would have a quiz on the material. After reading the passage, students in one condition were asked to continue
Recent research suggests that the amount of time that parents spend talking about numbers can have a big impact on the mathematical development of their children (Levine, Suriyakham, Rowe, Huttenlocher,& Gunderson, 2010). In the study, the researchers visited the children’s homes between the ages
Describe the F-ratio for the repeated-measures ANOVA and explain how it is related to the F-ratio for an independent-measures ANOVA.
Describe the two-stage structure of the repeated-measures ANOVA and explain what happens in each stage.
Calculate all of the SS, df, and MS values needed for a repeated-measures ANOVA and explain the relationships among them.
Conduct a complete repeated-measures ANOVA and a measure of effect size.
Describe how the results of a repeated-measures ANVOA are reported in the literature and explain how to determine the number of treatments and the number of participants from the reported df values for the F-ratio.
Describe the general advantages and disadvantages of repeated-measures versus independent-measures designs and identify the circumstances in which each is more appropriate.
Explain the relationship between the repeated-measures t test and a repeatedmeasures ANOVA when evaluating the difference between two means from a repeated-measures design.
Describe the structure of a factorial research design, especially a two-factor independent-measures design, using the terms factor and level and identify the factors and levels for a specic example of a two-factor design.
Dene a main effect and an interaction and identify the patterns of data that produce main effects and interactions.
Identify the three F-ratios for a two-factor ANOVA and explain how they are related to each other.
Describe the two-stage structure of a two-factor ANOVA and explain what happens in each stage.
Compute the SS, df, and MS values needed for a two-factor ANOVA, explain the relationships among them, and used the df values from a specic ANOVA to describe the structure of the study and the number of participants.
Conduct a two-factor ANOVA including measures of effect size for both main effects and the interaction.
Where are individual differences located in the F-ratio for a repeated-measures ANOVA?a. In both the numerator and the denominatorb. In the numerator but not in the denominatorc. In the denominator but not in the numeratord. There are no individual differences in the numerator and they have been
What happens to the variability due to individual differences in the F-ratio for a repeated-measures ANOVA?a. It is automatically eliminated from the numerator but must be computed and subtracted out of the denominator.b. It is automatically eliminated from the denominator but must be computed and
What happens during the second stage of a repeated-measures ANOVA?a. The variability from individual differences is measured and subtracted from the numerator of the F-ratio.b. The variability from individual differences is measured and subtracted from the denominator of the F-ratio.c. The
For a repeated-measures ANOVA, which of the following accurately defines the degrees of freedom for SSerror?a. n 2 1b. k 2 1c. (N 2 k) 2 (n 2 1)d. N 2 1
For the following data, what are the df values for the repeated-measures F-ratio?a. 2, 4b. 2, 6c. 3, 4d. 3, 6
The results of a repeated-measures ANOVA are reported as follows: F(3, 27) 5 1.12, p . .05. h2 5 0.17. How many participants were in the study?a. 40b. 36c. 10d. 9
Which of the following are advantages of a repeated-measures ANOVA compared to an independent-measures ANOVA?a. It requires fewer participants and reduces the risk of order effects such as practice or fatigue.b. It minimizes problems from individual differences and reduces the risk of order effects
A repeated-measures ANOVA produced an F-ratio of F 5 4.00 with df 5 1, 12.If the same data were analyzed with a repeated-measures t test, what df value would the t statistic have?a. 11b. 12c. 13d. Cannot be determined without more information
A two-factor study with two levels of factor A and three levels of factor B uses a separate sample of n 5 5 participants in each treatment condition. How many participants are needed for the entire study?a. 5b. 10c. 25d. 30
Which of the following accurately describes an interaction between two variables?a. The effect of one variable depends on the levels of the second variable.b. Both variables are equally inuenced by a third factor.c. The two variables are differentially affected by a third variable.d. Both
The results from a two-factor analysis of variance show that both main effects are significant. From this information, what can you conclude about the interaction?a. The interaction also must be signicant.b. The interaction cannot be signicant.c. There must be an interaction but it may not be
Which of the following accurately describes the two stages of a two-factor ANOVA?a. The rst stage partitions the total variability and the second stage partitions the within-treatment variability.b. The rst stage partitions the total variability and the second stage partitions the
In a two-factor analysis of variance, the F-ratio for factor A has df 5 2, 60 and the F-ratio for factor B has df 5 3, 60.Based on this information, what are the df values for the F-ratio for the interaction?a. 3, 60b. 5, 60c. 6, 60d. Cannot be determined without additional information
The following table shows the results for a repeated-measures ANOVA. Based on this table, what is the value for h2 for factor A?a. 12 36b. 12 96c. 12 99d. 12 120
What is the relationship between the F-ratio for a repeated-measures ANOVA and the F-ratio for an independent-measures ANOVA? Specifically, describe the role of individual differences in each.
A researcher conducts an experiment comparing four treatment conditions with n 5 12 scores in each condition.a. If the researcher uses an independent-measures design, how many individuals are needed for the study and what are the df values for the F-ratio?b. If the researcher uses a
A researcher conducts a repeated-measures experiment using a sample of n 5 15 subjects to evaluate the differences among three treatment conditions. If the results are examined with an ANOVA, what are the df values for the F-ratio?
The following data were obtained from a repeatedmeasures study comparing three treatment conditions.Use a repeated-measures ANOVA with a 5.05 to determine whether there are significant mean differences among the three treatments.Treatments Person I II III Person Totals A 0 2 4 P = 6 B 0 3 6 P = 9 N
The following data represent the results of a repeated-measures study comparing different viewing distances for a 42-inch, high-definition television.Four viewing distances were evaluated: 9 feet, 12 feet, 15 feet, and 18 feet. Each participant was free to move back and forth among the four
One of the advantages of a repeated-measures design is that it removes individual differences from the error variance and increases the likelihood of rejecting the null hypothesis. The following data were obtained from a research study comparing three treatment conditions.I II III 6 8 10 G = 48 5 5
The following summary table presents the results from a repeated-measures ANOVA comparing three treatment conditions with a sample of n 5 8 participants.Fill in the missing values in the table. (Hint: Start with the df values.)Source SS df MS Between treatments _____ _____ _____ F 5 6.50 Within
The following summary table presents the results from a repeated-measures ANOVA comparing four treatment conditions, each with a sample of n 5 20 participants. Fill in the missing values in the table.(Hint: Start with the df values.)Source SS df MS Between treatments 33 _____ _____ F 5_____ Within
A researcher uses a repeated-measures ANOVA to evaluate the results from a research study and reports an F-ratio with df 5 3, 24.a. How many treatment conditions were compared in the study?b. How many individuals participated in the study?
A published report of a repeated-measures research study includes the following description of the statistical analysis: “The results show significant differences among the treatment conditions, F(2, 26) 5 4.87, p , .05.”a. How many treatment conditions were compared in the study?b. How many
The following data are from a repeated-measures study comparing three treatment conditions.a. Use a repeated-measures ANOVA with a 5.05 to determine whether there are significant differences among the treatments and compute h2 to measure the size of the treatment effect.b. Double the number of
The following data are from a repeated-measures study comparing two treatment conditions.a. Use a repeated-measures ANOVA with a 5.05 to determine whether the mean difference between treatments is significant.b. Now use a repeated-measures t test with a 5.05 to evaluate the mean difference between
In Problem 6 at the end of Chapter 11 (page 325), we presented a study showing that a visible tattoo can significantly lower the attractiveness rating of a woman shown in a photograph (Resenhoeft, Villa, &Wiseman, 2008). In a similar study, a sample of n 5 9 males looks at a set of 30 photographs
For the data in the following matrix:No Treatment Treatment Male M = 8 M = 14 Overall M =11 Female M = 4 M = 10 Overall M = 7 overall M = 6 overall M = 12a. Which two means are compared to describe the treatment main effect?b. Which two means are compared to describe the gender main effect?c. Is
The following matrix presents the results from an independent-measures, two-factor study with a sample of n 5 10 participants in each treatment condition.Note that one treatment mean is missing.Factor B Factor A B1 B2 A1 M = 3 M = 7 A2 M = 5a. What value for the missing mean would result in no main
The following matrix presents the results of a twofactor study with n 5 10 scores in each of the six treatment conditions. Note that one of the treatment means is missing.Factor B B1 B2 B3 Factor A A1 M = 4 M = 6 M = 14 A2 M = 2 M = 4a. What value for the missing mean would result in no main effect
A researcher conducts an independent-measures, twofactor study with two levels of factor A and two levels of factor B, using a sample of n 5 8 participants in each treatment condition.a. What are the df values for the F-ratio evaluating the main effect of factor A?b. What are the df values for the
The following results are from an independent-measures, two-factor study with n 5 10 participants in each treatment condition.Factor B B1 B2 Factor A A1 T = 40 T = 10 M = 4 M = 1 SS = 50 SS = 30 A2 T = 50 T = 20 M = 5 M = 2 SS = 60 SS = 40 N = 40 G = 120ΣX2 = 640a. Use a two-factor ANOVA with a 5
The following results are from an independent-measures, two-factor study with n 5 5 participants in each treatment condition. Use a two-factor ANOVA with a 5 .05 to evaluate the main effects and the interaction.Factor B B1 B2 B3 Factor A A1 T = 25 T = 40 T = 70 M = 5 M = 8 M = 14 SS = 30 SS = 38 SS
Most sports injuries are immediate and obvious, like a broken leg. However, some can be more subtle, like the neurological damage that may occur when soccer players repeatedly head a soccer ball. To examine effects of repeated heading, McAllister et al. (2013)examined a group of football and ice
The following table summarizes the results from a two-factor study with two levels of factor A and four levels of factor B using a separate sample of n 5 5 participants in each treatment condition. Fill in the missing values. (Hint: Start with the df values.)Source SS df MS Between treatments _____
The following table summarizes the results from a two-factor study with two levels of factor A and three levels of factor B using a separate sample of n 5 8 participants in each treatment condition. Fill in the missing values. (Hint: Start with the df values.)Source SS df MS Between treatments 72
Earlier in this chapter we described a study by Bartholow and Anderson (2002) examining how the experience of violence in video games influenced aggressive behavior for males and females. Their results suggest that increased violence increase aggressive behavior for males but has little or no
Describe the circumstances in which a t statistic is used for hypothesis testing instead of a z-score and explain the fundamental difference between a t statistic and a z-score for a sample mean.
Calculate the estimated standard error of M for a specic sample size and sample variance, and explain what it measures.
Explain the relationship between the t distribution and the normal distribution.
Conduct a hypothesis test using the t statistic.
Explain how the likelihood of rejecting the null hypothesis for a t test is inuenced by sample size and sample variance.
Calculate Cohen’s d or the percentage of variance accounted for (r2) to measure effect size for a hypothesis test with a t statistic.
Explain how measures of effect size for a t test are inuenced by sample size and sample variance.
Explain how a condence interval can be used to describe the size of a treatment effect for a test and describe the factors that affect the width of a condence interval.
Describe how the results from a hypothesis test using a t statistic are reported in the literature.
Conduct a directional (one-tailed) hypothesis test using the t statistic.
In what circumstances is the t statistic used instead of a z-score for a hypothesis test?a. The t statistic is used when the sample size is n 5 30 or larger.b. The t statistic is used when the population mean is unknown.c. The t statistic is used when the population variance (or standard
A sample of n 5 4 scores has SS 5 48.What is the estimated standard error for the sample mean?a. 48b. 16c. 4d. 2
On average, what value is expected for the t statistic when the null hypothesis is true?a. 0b. 1c. 1.96d. t . 1.96
A sample of n 5 9 scores is selected from a population with a mean of m 5 70, and a treatment is administered to the sample. After treatment, the sample has M 5 74 and SS 5 288.If a hypothesis test with a t statistic is used to evaluate the treatment effect, then what value will be obtained for the
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