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essentials of statistics

Questions and Answers of Essentials Of Statistics

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
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
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.
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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:
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
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
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
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
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
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
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
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
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
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
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
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
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.
Explain how measures of effect size such as Cohen’s d are inuenced by the sample size and the standard deviation.
Dene the power of a hypothesis test and explain how power is related to the probability of a Type II error.
Identify the factors that inuence power and explain how power is affected by each.
In general terms, what is a hypothesis test?a. A descriptive technique that allows researchers to describe a sampleb. A descriptive technique that allows researchers to describe a populationc. An
A sample is selected from a population with a mean of m 5 60 and a treatment is administered to the individuals in the sample. If a hypothesis test is used to evaluate the treatment effect, then what
Which of the following accurately describes the critical region for a hypothesis test?a. Outcomes that have a very low probability if the null hypothesis is trueb. Outcomes that have a high
A sample of n 5 25 individuals is selected from a population with m 5 80 and a treatment is administered to the sample. Which of the following is the most likely outcome if the treatment has a large
What does a Type II error mean?a. A researcher has falsely concluded that a treatment has an effect.b. A researcher has correctly concluded that a treatment has no effect.c. A researcher has falsely
Which of the following defines a Type I error?a. Rejecting a false null hypothesisb. Rejecting a true null hypothesisc. Failing to reject a false null hypothesisd. Failing to reject a true null
What is the consequence of increasing the alpha level (for example, from .01 to.05)?a. It will increase the likelihood of rejecting H0 and increase the risk of a Type I error.b. It will decrease the
A research report includes the statement, “z 5 2.18, p , .05.” What happened in the hypothesis test?a. The obtained sample mean was very unlikely if the null hypothesis is true, so H0 was
A sample of n 5 4 individuals is selected from a population with m 5 80 and s 5 5, and a treatment is administered to the sample. If the treatment really does have an effect, then what would be the
What assumption is needed before you can use the unit normal table to find critical values for a z-score hypothesis test?a. The population of scores before treatment is normal.b. The scores are
A population is known to have a mean of m 5 50.A treatment is expected to increase scores for individuals in this population. If the treatment is evaluated using a one-tailed hypothesis, then which

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