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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

A researcher uses analysis of variance to test for mean differences among four treatments with a sample of n 5 6 in each treatment. The F-ratio for this analysis would have what df values?a. df 5 3, 5b. df 5 3, 15c. df 5 3, 20d. df 5 4, 24
The following table shows the results of an analysis of variance comparing two treatment conditions with a sample of n 5 11 participants in each treatment.Note that several values are missing in the table. What is the missing value for the F-ratio?a. 2b. 7c. 14d. 28
A research report concludes that there are significant differences among treatments, with “F(2, 27) 5 8.62, p , .01, h2 5 0.46.” How many treatment conditions were compared in this study?a. 2b. 3c. 29d. 30
Under what circumstances are post hoc tests necessary after an ANOVA?a. When H0 is rejectedb. When there are more than two treatmentsc. When H0 is rejected and there are more than two treatmentsd. You always should do post hoc tests after an ANOVA.
An ANOVA finds significant treatment effects for a study comparing three treatments with means of M1 5 8, M2 5 4, M3 5
If Tukey’s HSD is computed to be HSD 5 2.50, then which of the treatments are significantly different?a. 1 vs. 2 and 2 vs. 3b. 1 vs. 2 and 1 vs. 3c. 1 vs. 3 and 2 vs. 3d. 1 vs. 2 and 1 vs. 3 and 2 vs. 3
Which combination of factors is most likely to produce a large value for the F-ratio and a large value for h2?a. Large mean differences and large sample variancesb. Large mean differences and small sample variancesc. Small mean differences and large sample variancesd. Small mean differences and
If an analysis of variance is used for the following data, what would be the effect of changing the value of M2 to 30?a. Increase SSbetween and increase the size of the F-ratiob. Increase SSbetween and decrease the size of the F-ratioc. Decrease SSbetween and increase the size of the F-ratiod.
A researcher uses an ANOVA to evaluate the mean difference between two treatment conditions and obtains F 5 4.00 with df 5 1, 16.If an independentmeasures t statistic had been used instead of the ANOVA, then what t value would be obtained and what is the df value for t?a. t 5 2.00 with df 5 16b. t
Calculate SStotal, SSbetween, and SSwithin for the following set of data:Treatment 1 Treatment 2 Treatment 3 n 5 10 n 5 10 n 5 10 N 5 30 T 5 10 T 5 20 T 5 30 G 5 60 SS 5 27 SS 5 16 SS 5 23 ΣX2 5 206
A researcher uses an ANOVA to compare three treatment conditions with a sample of n 5 8 in each treatment. For this analysis, find dftotal, dfbetween, and dfwithin.
A researcher reports an F-ratio with dfbetween 5 2 and dfwithin 5 30 for an independent-measures ANOVA.a. How many treatment conditions were compared in the experiment?b. How many subjects participated in the experiment?
A researcher reports an F-ratio with df 5 3, 24 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?
The following values are from an independent-measures study comparing three treatment conditions.Treatment I II III n 5 8 n 5 8 n 5 8 SS 5 35 SS 5 42 SS 5 70a. Compute the variance for each sample.b. Compute MSwithin, which would be the denominator of the F-ratio for an ANOVA.Because the samples
A researcher conducts an experiment comparing four treatment conditions with a separate sample of n 5 6 in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the following table. Complete all missing values in the table. Hint: Begin with the values
The following summary table presents the results from an ANOVA comparing four treatment conditions with n 5 10 participants in each condition.Complete all missing values. (Hint: Start with the df column.)Source SS df MS Between treatments ____ ____ 10 F 5 ____ Within treatments ____ ____ ____ Total
A developmental psychologist is examining the development of language skills from age 2 to age 4.Three different groups of children are obtained, one for each age, with n 5 18 children in each group. Each child is given a language-skills assessment test. The resulting data were analyzed with an
The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with a 5 .05 to determine whether there are any significant mean differences among the treatments.Treatment I II III 5 2 7 1 6 3 2 2 2 3 3 4 0 5 5 1 3 2 2 0 4 2 3 5
The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with a 5 .05 to determine whether there are any significant mean differences among the treatments.Treatment I II III n 5 8 n 5 6 n 5 4 N 5 18 T 5 16 T 5 24 T 5 32 G 5 72
A research study comparing three treatment conditions produces T 5 20 with n 5 4 for the first treatment, T 5 10 with n 5 5 for the second treatment, and T 5 30 with n 5 6 for the third treatment. Calculate SSbetween treatments for these data.
The following values are from an independent-measures study comparing three treatment conditions.Treatments I II III n 5 8 n 5 8 n 5 8 SS 5 42 SS 5 28 SS 5 98a. Compute the variance for each sample.b. Compute MSwithin, which would be the denominator of the F-ratio for an ANOVA. Because the samples
A research report from an independent-measures study states that there are significant differences between treatments, F(2, 36) 5 3.45, p , .05.a. How many treatment conditions were compared in the study?b. What was the total number of participants in the study?
A researcher used ANOVA and computed F 5 4.25 for the following data.Treatments I II III n 5 10 n 5 10 n 5 10 M 5 20 M 5 28 M 5 35 SS 5 1,005 SS 5 1,391 SS 5 1,180a. If the mean for Treatment III were changed to M 5 25, what would happen to the size of the F-ratio (increase or decrease)? Explain
The following data were obtained from an independentmeasures study comparing three treatment conditions.Treatment I II III n 5 6 n 5 6 n 5 6 N 5 18 M 5 1 M 5 2 M 5 6 G 5 54 SS 5 60 SS 5 65 SS 5 40 SX2 5 411a. Calculate the sample variance for each of the three samples.b. Use an ANOVA with a 5 .05
For the preceding problem you should find that there are significant differences among the three treatments.One reason for the significance is that the sample variances are relatively small. To create the following data, we kept the same sample means that appeared in problem 19 but doubled the SS
The following data summarize the results from an independent-measures study comparing three treatment conditions.Treatment I II III n 5 5 n 5 5 n 5 5 M 5 1 M 5 5 M 5 6 N 5 15 T 5 5 T 5 25 T 5 30 G 5 60 s 2 5 9.00 s 2 5 10.00 s 2 5 11.00 SX2 5 430 SS 5 36 SS 5 40 SS 5 44a. Use an ANOVA with a 5 .05
To create the following data we started with the same sample means and variances that appeared in problem 21 but doubled the sample size to n 5 10.Treatment I II III n 5 10 n 5 10 n 5 10 M 5 1 M 5 5 M 5 6 N 5 30 T 5 10 T 5 50 T 5 60 G 5 120 s2 5 9.00 s 2 5 10.00 s 2 5 11.00 SX2 5 890 SS 5 81 SS 5
Use an ANOVA with a 5 .05 to check your prediction. Note: Because the samples are all the same size, MSwithin is the average of the three sample variances.b. Predict how the increase in sample size should affect the value of h2 for these data compared to the h2 in problem 21.Calculate h2 to check
An ANOVA produces an F-ratio with df 5 1, 34.Could the data have been analyzed with a t test? What would be the degrees of freedom for the t statistic?
The following scores are from an independentmeasures study comparing two treatment conditions.a. Use an independent-measures t test with a 5 .05 to determine whether there is a significant mean difference between the two treatments.b. Use an ANOVA with a 5 .05 to determine whether there is a
Dene variability and explain its use and importance as a statistical measure.
Dene and calculate the range as a simple measure of variability and explain its limitations
Dene variance and standard deviation and describe what is measured by each.
Calculate variance and standard deviation for a simple set of scores.
Estimate the standard deviation for a set of scores based on a visual examination of a frequency distribution graph of the distribution.
Calculate SS, the sum of the squared deviations, for a population using either the denitional or the computational formula and describe the circumstances in which each formula is appropriate.
Calculate the variance and the standard deviation for a population.
Explain why it is necessary to make a correction to the formulas for variance and standard deviation when computing these statistics for a sample.
Calculate SS, the sum of the squared deviations, for a sample using either the denitional or the computational formula and describe the circumstances in which each formula is appropriate.
Calculate the variance and the standard deviation for a sample.
Dene biased and unbiased statistics.
Explain why the sample mean and the sample variance (dividing by n 2 1) are unbiased statistics.
Describe how the mean and standard deviation are represented in a frequency distribution graph of a population or sample distribution.
Describe the effect on the mean and standard deviation and calculate the outcome for each of the following: adding or subtracting a constant from each score, and multiplying or dividing each score by a constant.
Describe how the mean and standard deviation are reported in research journals.
Determine the general appearance of a distribution based on the values for the mean and standard deviation.
Explain how patterns in sample data are affected by sample variance
Which of the following is a consequence of increasing variability?a. The distance from one score to another tends to increase and a single score tends to provide a more accurate representation of the entire distribution.b. The distance from one score to another tends to increase and a single score
What is the range for the following set of scores? Scores: 5, 7, 9, 15a. 4 pointsb. 5 pointsc. 10 or 11 pointsd. 15 points
For the following scores, which of the following actions will increase the range? Scores: 3, 7, 10, 15a. Add 4 points to the score X 5 3b. Add 4 points to the score X 5 7c. Add 4 points to the score X 5 10d. Add 4 points to the score X 5 15
Which of the following sets of scores has the largest variance?a. 1, 3, 8, 12b. 12, 13, 14, 15c. 2, 2, 2, 2d. 22, 24, 25, 27
What is the variance for the following set of scores? Scores: 4, 1, 7a. 66 3 5 22b. 18c. 9d. 6
A set of scores ranges from a high of X 5 24 to a low of X 5 12 and has a mean of 18.Which of the following is the most likely value for the standard deviation for these scores?a. 3 pointsb. 6 pointsc. 12 pointsd. 24 points.
What is SS, the sum of the squared deviations, for the following population of N 5 5 scores? Scores: 1, 9, 0, 2, 3a. 10b. 41c. 50d. 95
What is the standard deviation for the following population of scores?Scores: 1, 3, 9, 3a. 36b. 9c. 6d. 3
A population of N 5 8 scores has a standard deviation of s 5
What is the value of SS, the sum of the squared deviations, for this population?a. 72b. 24c. 8Ï3d. 9 8 5 1.125
Which of the following explains why it is necessary to make a correction to the formula for sample variance?a. If sample variance is computed by dividing by n, instead of n 2 1, the resulting values will tend to underestimate the population variance.b. If sample variance is computed by dividing by
Under what circumstances is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a sample?a. When the sample mean is a whole numberb. When the sample mean is not a whole numberc. When the sample variance is a whole numberd. When
What is the variance for the following sample of n 5 5 scores? Scores: 2, 0, 8, 2, 3a. 81 4 5 20.25b. 36 4 5 9c. 36 5 5 7.2d. Ï9 5 3
A researcher takes a sample from a population and computes a statistic for the sample. Which of the following statements is correct?a. If the sample statistic overestimates the corresponding population parameter, then the statistic is biased.b. If the sample statistic underestimates the
A researcher takes all of the possible samples of n 5 4 from a population.Next, the researcher computes a statistic for each sample and calculates the average of all the statistics. Which of the following statements is the most accurate?a. If the average statistic overestimates the corresponding
All the possible samples of n 5 3 scores are selected from a population with m 5 30 and s 5 5 and the mean is computed for each of the samples. If the average is calculated for all of the sample means, what value will be obtained?a. 30b. Greater than 30c. Less than 30d. Near 30 but not exactly
If a normal-shaped population with m 5 40 and s 5 5 is shown in a frequency distribution graph, how would the mean and standard deviation be represented?a. The mean is represented by a vertical line drawn at X 5 40 and the standard deviation is represented by a vertical line drawn at X 5 45.b. The
If 5 points are added to every score in a population with a mean of m 5 45 and a standard deviation of s 5 6, what are the new values for m and s?a. m 5 45 and s 5 6b. m 5 45 and s 5 11c. m 5 50 and s 5 6d. m 5 50 and s 5 11
A research study obtains a mean of 12.7 and a standard deviation of 2.3 for a sample of n 5 25 participants. How would the sample mean and standard deviation be reported in a research journal report?a. M 5 12.7 and s 5 2.3b. M 5 12.7 and SD 5 2.3c. Mn 5 12.7 and s 5 2.3d. Mn 5 12.7 and SD 5 2.3
For which of the following distributions would X 5 35 be an extreme score?a. m 5 30 and s 5 5b. m 5 30 and s 5 10c. m 5 25 and s 5 5d. m 5 25 and s 5 10
One sample is selected to represent scores in treatment 1 and a second sample is used to represent scores in treatment 2.Which set of sample statistics would present the clearest picture of a real mean difference between the two treatments?a. M1 5 40, M2 5 45, and both variances 5 15b. M1 5 40, M2
In words, explain what is measured by variance and standard deviation.
Is it possible to obtain a negative value for variance or standard deviation?
Calculate the mean and SS (sum of squared deviations)for each of the following sets of scores. Based on the value for the mean, you should be able to decide which SS formula is better to use.Set A: 2, 6, 3, 1 Set B: 2, 4, 1, 3
For the following population of N 5 9 scores: 4, 2, 0, 5, 3, 2, 1, 7, 3a. Sketch a histogram showing the population distribution.b. Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.2).c. Compute SS, variance, and standard
Calculate SS, variance, and standard deviation for the following population of N 5 5 scores: 2, 13, 4, 10, 6.(Note: The definitional formula works well with these scores.)
Calculate SS, variance, and standard deviation for the following population of N 5 8 scores: 1, 3, 1, 10, 1, 0, 1, 3.(Note: The computational formula works well with these scores.)
Calculate SS, variance, and standard deviation for the following population of N 5 7 scores: 8, 1, 4, 3, 5, 3, 4.(Note: The definitional formula works well with these scores.)
Explain why the formula for sample variance is different from the formula for population variance.
For the following sample of n 5 6 scores:0, 11, 5, 10, 5, 5a. Sketch a histogram showing the sample distribution.b. Locate the value of the sample mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.6).c. Compute SS, variance, and standard deviation for the
Calculate SS, variance, and standard deviation for the following sample of n 5 8 scores: 0, 4, 1, 3, 2, 1, 1, 0.
A population has a mean of m 5 50 and a standard deviation of s 5 10.a. If 3 points were added to every score in the population, what would be the new values for the mean and standard deviation?b. If every score in the population were multiplied by 2, then what would be the new values for the mean
Solve the following problems.a. After 6 points have been added to every score in a sample, the mean is found to be M 5 70 and the standard deviation is s 513.What were the values for the mean and standard deviation for the original sample?b. After every score in a sample is multiplied by 3, the
What were the values for the mean and standard deviation for the original sample?
Compute the mean and standard deviation for the following sample of n 5 5 scores: 70, 72, 71, 80, and 72.Hint: To simplify the arithmetic, you can subtract 70 points from each score to obtain a new sample.Then, compute the mean and standard deviation for the new sample. Finally, make the correction
For the following sample of n 5 8 scores: 0, 1, 1 2, 0, 3, 1 2, 0, 1a. Simplify the arithmetic by first multiplying each score by 2 to obtain a new sample. Then, compute the mean and standard deviation for the new sample.b. Starting with the values you obtained in part a, make the correction for
For the following population of N 5 6 scores: 2, 9, 6, 8, 9, 8a. Calculate the range and the standard deviation. (Use either definition for the range.)b. Add 2 points to each score and compute the range and standard deviation again. Describe how adding a constant to each score influences measures
The range is completely determined by the two extreme scores in a distribution. The standard deviation, on the other hand, uses every score.a. Compute the range (choose either definition), the variance, and the standard deviation for the following sample of n 5 4 scores. Note that there are two
For the data in the following sample: 1, 1, 9, 1a. Find the SS, variance, and standard deviation.b. Now change the score of X 5 9 to X 5 3, and find the new values for SS, variance, and standard deviation.c. Describe how one extreme score influences the mean and standard deviation.
Arden and Plomin (2006) published a study reporting that IQ scores for boys are more variable than IQ scores for girls. A researcher would like to know if this same phenomenon applies to other measures of cognitive ability. A standard cognitive skills test is given to a sample of n 5 15 adolescent
A population has a mean of m 5 50 and a standard deviation of s 5 20.a. Would a score of X 5 70 be considered an extreme value (out in the tail) in this sample?b. If the standard deviation were s 5 5, would a score of X 5 70 be considered an extreme value?
On an exam with a mean of M 5 39, you obtain a score of X 5 35.a. Would you prefer a standard deviation of s 5 2 or s 5 8? (Hint: Sketch each distribution and find the location of your score.)b. If your score were X 5 43, would you prefer s 5 2 or s 5 8? Explain your answer.
Describe the purpose of a hypothesis test and explain how the test accomplishes its goal.
Dene the null hypothesis and the alternative hypothesis for a hypothesis test, and determine each for a specic research example.
Dene the alpha level (level of signicance) and the critical region for a hypothesis test and explain how the outcome of a hypothesis test is inuenced by a change in alpha level.
Conduct a hypothesis test using the standard 4-step procedure and make a statistical decision about the effect of a treatment.
Dene a Type I error and a Type II error, explain the consequences of each, and describe how a Type I error is related to the alpha level.
Describe how the results of a hypothesis test with a z-score test statistic are reported in the literature.
Explain how the outcome of a hypothesis test is inuenced by the sample size, the standard deviation, and the difference between the sample mean and the hypothesized population mean.
Describe the assumptions underlying a hypothesis test with a z-score test statistic.
Describe the hypotheses and the critical region for a directional (one-tailed) hypothesis test.
Explain why it is necessary to report a measure of effect size in addition to the outcome of a hypothesis test.
Calculate Cohen’s d as a measure of effect size.

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