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essentials of statistics

Questions and Answers of Essentials Of Statistics

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.
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
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
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.
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
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
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
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
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
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,
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
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.
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
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,
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
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
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
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
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
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
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
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.
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
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
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
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.
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
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
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
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
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
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
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.
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
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
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,
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 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
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,
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 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
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
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
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
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
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
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.
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.
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
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
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
A hypothesis test produces a t statistic of t 5 2.30. If the researcher is using a two-tailed test with a 5 .05, how large does the sample have to be in order to reject the null hypothesis?a. at
A sample is selected from a population and a treatment is administered to the sample. For a hypothesis test with a t statistic, if there is a 5-point difference between the sample mean and the
A sample of n 5 25 is selected from a population with m 5 40, and a treatment is administered to each individual in the sample. After treatment, the sample mean is M 5 44 with a sample variance of s
A sample is selected from a population with a mean of m 5 75, and a treatment is administered to the individuals in the sample. The researcher intends to use a t statistic to evaluate the effect of
A sample of n 5 4 scores is selected from a population with an unknown mean. The sample has a mean of M 5 40 and a variance of s 2 5 16.Which of the following is the correct 90% confidence interval
A researcher uses a sample of n 5 25 individuals to evaluate the effect of a treatment. The hypothesis test uses a 5 .05 and produces a significant result with t 5 2.15. How would this result be
A sample is selected from a population with a mean of m 5 30 and a treatment is administered to the sample. If the treatment is expected to increase scores and a t statistic is used for a one-tailed
A researcher predicts that a treatment will increase scores. To test the treatment effect, a sample of n 5 16 is selected from a population with m 5 80 and a treatment is administered to the
A researcher fails to reject the null hypothesis with a regular two-tailed test using a 5 .05. If the researcher used a directional (one-tailed) test with the same data and the same alpha level, then
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?
A sample of n 5 16 scores has a mean of M 5 56 and a standard deviation of s 5 20.a. Explain what is measured by the sample standard deviation.b. Compute the estimated standard error for the sample
Find the estimated standard error for the sample mean for each of the following samples.a. n 5 9 with SS 5 1152b. n 5 16 with SS 5 540c. n 5 25 with SS 5 600
The following sample of n 5 4 scores was obtained from a population with unknown parameters. Scores:2, 2, 6, 2a. Compute the sample mean and standard deviation.(Note that these are descriptive values
The following sample was obtained from a population with unknown parameters. Scores: 13, 7, 6, 12, 0, 4a. Compute the sample mean and standard deviation.(Note that these are descriptive values that

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