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essentials of statistics

Questions and Answers of Essentials Of Statistics

A researcher is conducting an experiment to evaluate a treatment that is expected to decrease the scores for individuals in a population which is known to have a mean of m 5 80.The results will be
A researcher expects a treatment to produce an increase in the population mean. Assuming a normal distribution, what is the critical z-score for a onetailed test with a 5 .01?a. 12.33b. 62.58c.
Under what circumstances can a very small treatment effect be statistically significant?a. With a large sample and a large standard deviationb. With a large sample and a small standard deviationc.
A sample of n 5 9 scores is selected from a population with a mean of m 5 80 and s 5 12, and a treatment is administered to the sample. After the treatment, the researcher measures effect size with
If other factors are held constant, then how does sample size affect the likelihood of rejecting the null hypothesis and the value for Cohen’s d?a. A larger sample increases the likelihood of
If the power of a hypothesis test is found to be p 5 0.80, then what is the probability of a Type II error for the same test?a. p 5 0.20b. p 5 0.80c. The probability of a Type II error is not related
How does the sample size influence the likelihood of rejecting the null hypothesis and the power of the hypothesis test?a. Increasing sample size increases both the likelihood of rejecting H0 and the
How is the power of a hypothesis test related to sample size and the alpha level?a. A larger sample and a larger alpha level will both increase power.b. A larger sample and a larger alpha level will
Identify the four steps of a hypothesis test as presented in this chapter.
Define the alpha level and the critical region for a hypothesis test.
Define a Type I error and a Type II error and explain the consequences of each.
If the alpha level is changed from a 5 .05 to a 5 .01,a. what happens to the boundaries for the critical region?b. what happens to the probability of a Type I error?
Explain how each of the following influences the value of the z-score in a hypothesis test.a. Increasing the difference between the sample mean and the original population meanb. Increasing the
Ackerman and Goldsmith (2011) report that students who study from a screen (phone, tablet, or computer) tended to have lower quiz scores than students who studied the same material from printed
Babcock and Marks (2010) review survey data from 2003–2005, and obtained an average of m 5 14 hours per week spent studying by full-time students at four-year colleges in the United States. To
Childhood participation in sports, cultural groups, and youth groups appears to be related to improved selfesteem for adolescents (McGee, Williams, HowdenChapman, Martin, & Kawachi, 2006). In a
The psychology department is gradually changing its curriculum by increasing the number of online course offerings. To evaluate the effectiveness of this change,a random sample of n 5 36 students who
A random sample is selected from a normal population with a mean of m 5 40 and a standard deviation of s 5 6.After a treatment is administered to the individuals in the sample, the sample mean is
A random sample of n 5 16 scores is selected from a normal population with a mean of m 5 50.After a treatment is administered to the individuals in the sample, the sample mean is found to be M 5
In a study examining the effect of humor on interpersonal attractions, McGee and Shevlin (2009) found that a man’s sense of humor had a significant effect on how he was perceived by women. In the
A random sample is selected from a normal population with a mean of m 5 40 and a standard deviation of s 5 10.After a treatment is administered to the individuals in the sample, the sample mean is
Researchers at a National Weather Center in the northeastern United States recorded the number of 90° Fahrenheit days each year since records first started in 1875. The numbers form a normal-shaped
A high school teacher has designed a new course intended to help students prepare for the mathematics section of the SAT. A sample of n 5 20 students is recruited for the course and, at the end of
Miller (2008) examined the energy drink consumption of college undergraduates and found that males use energy drinks significantly more often than females.To further investigate this phenomenon,
After examining over one million online restaurant reviews and the associated weather conditions, Bakhshi, Kanuparthy, and Gilbert (2014) reported significantly higher ratings during moderate weather
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of m 5 40 and a standard deviation of s 5 12.The researcher expects
A researcher plans to conduct an experiment evaluating the effect of a treatment. A sample of n 5 9 participants is selected and each person receives the treatment before being tested on a
Research has shown that IQ scores have been increasing for years (Flynn, 1984, 1999). The phenomenon is called the Flynn effect and the data indicate that the increase appears to average about 7
Evaluate each of the following expressions:a. 4 3 8/22b. 4 3 (8/2)2c. 100 2 3 3 12/(6 2 4)2d. (4 1 6) 3 (3 2 1)2e. (8 2 2)/(9 2 8)2f. 6 1 (4 2 1)2 2 3 3 42 g. 4 3 (8 2 3) 1 8 2 3
Convert 3 25 to a decimal.
Convert 3 8 to a percentage.
Next to each set of fractions, write “True” if they are equivalent and “False” if they are not:a. 3 8 5 9 24b. 7 9 5 17 19c. 2 7 5 4 14
Compute the following:a. 1 6 3 7 10b. 7 8 2 1 2c. 9 10 4 2 3d. 7 22 1 2 3
Identify the larger fraction of each pair:a. 7 10, 21 100b. 3 4, 7 12c. 22 3 , 19 3
Convert the following decimals into fractions:a. 0.012b. 0.77c. 0.005
2.59 3 0.015 5 ?
1.8 4 0.02 5 ?
What is 28% of 45?
Complete the following calculations:a. 3 1 (28) 1 5 1 7 1 (21) 1 (23)b. 5 2 (29) 1 2 2 (23) 2 (21)c. 3 2 7 2 (221) 1 (25) 2 (29)d. 4 2 (26) 2 3 1 11 2 14e. 9 1 8 2 2 2 1 2 (26)f. 9 3 (23)g. 27 3
Dene a repeated-measures design, explain how it differs from an independentmeasures design, and identify examples of each.
Describe the data (difference scores) that are used for the repeated-measures t statistic.
Determine the hypotheses for a repeated-measures t test.
Describe the structure of the repeated-measures t statistic, including the estimated standard error and the degrees of freedom, and explain how the formula is related to the single-sample t.
Calculate the estimated standard error for the mean of the difference scores and explain what it measures.
Conduct a repeated-measures t test to evaluate the signicance of the population mean difference using the data from a repeated-measures study comparing two treatment conditions.
Conduct a directional (one-tailed) hypothesis test using the repeated-measures t statistic.
Measure effect size for a repeated-measures t test using either Cohen’s d or r 2, the percentage of variance accounted for.
Use the data from a repeated-measures study to compute a condence interval describing the size of the population mean difference.
Describe how the results of a repeated-measures t test and measures of effect size are reported in the scientic literature.
Describe how the outcome of a hypothesis test and measures of effect size using the repeated-measures t statistic are inuenced by sample size and sample variance.
Describe how the consistency of the treatment effect is reected in the variability of the difference scores and explain how this inuences the outcome of a hypothesis test.
Describe the advantages and disadvantages of choosing a repeated-measures design instead of an independent-measures design to compare two treatment conditions, and with that information in mind,
Dene a matched-subjects design and explain how it differs from repeated-measures and independent-measures designs.
In a repeated-measures study, the same group of individuals participates in all of the treatment conditions. Which of the following situations is not an example of a repeated-measures design?a. A
A researcher conducts a research study comparing two treatment conditions and obtains 20 scores in each treatment. If the researcher used a repeated-measures design, then how many subjects
For an experiment comparing two treatment conditions, an independentmeasures design would obtain ____ score(s) for each subject and a repeatedmeasures design would obtain ____ score(s) for each
What is the mean for the difference scores for the following data from a repeated-measures study?a. 5b. 6c. 11d. 44
Which of the following is the correct statement of the null hypothesis for a repeated-measures hypothesis test?a. MD 5 0b. mD 5 0c. m1 5 m2d. M1 5 M2
Which of the following accurately describes the relationship between the repeated-measures t statistic and the single-sample t statistic?a. Each uses one sample mean.b. Each uses one population
What is the value for the estimated standard error for a set of n 5 9 difference scores with SS 5 72?a. 72b. 9c. 3d. 1
A researcher conducts a repeated-measures study comparing two treatment conditions with a sample of n 5 25 participants and obtains a t statistic of t 5 2.21. Which of the following is the correct
A researcher is using a one-tailed hypothesis test to evaluate the significance of a mean difference between two treatments in a repeated-measures study. If the treatment is expected to increase
The results of a repeated-measures study with n 5 25 participants produce a mean difference of MD 5 1.2 points with SS 5 96 for the difference scores and a t statistic of t 5 3.00. If the percentage
For a repeated-measures study with n 5 12 scores in each treatment, a researcher constructs an 80% confidence interval to describe the mean difference between treatments. What value is at the center
A research report describing the results from a repeated-measures study states,“The data showed a significant difference between treatments, t(22) 5 4.71, p , .01.” From this report, what can you
A repeated-measures study finds a mean difference of MD 5 5 points between two treatment conditions. Which of the following sample characteristics is most likely to produce a significant t statistic
If the results of a repeated-measures study show that nearly all of the participants score around 5 points higher in Treatment A than in Treatment B, then which of the following accurately describes
Which of the following possibilities is a concern with a repeated-measures study?a. Negative values for the difference scoresb. Carry-over effectsc. Obtaining a mean difference that is due to
For which of the following situations would an independent-measures design have the maximum advantage over a repeated-measures design?a. When individual differences are small and participating in one
A matched-subjects study comparing two treatments with 10 scores in each treatment requires a total of ___ participants and measures ___ score(s) for each individual.a. 10, 1b. 10, 2c. 20, 1d. 20, 2
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
What is the defining characteristic of a repeated-measures or within-subjects research design?
A researcher conducts an experiment comparing two treatment conditions with 15 scores in each treatment condition.a. If an independent-measures design is used, how many subjects are needed for the
A repeated-measures and an independent-measures study both produce a t statistic with df 5 20.How many subjects participated in each experiment?
A sample of n 5 16 individuals participates in a repeated-measures study that produces a sample mean difference of MD 5 6.45 with SS 5 960 for the difference scores.a. Calculate the standard
Resenhoeft, Villa, and Wiseman (2008) conducted a study showing that a woman shown in a photograph was judged as less attractive when the photograph showed a visible tattoo compared to the same
The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of n 5 9 participants before and after they receive the treatment.a. Calculate the
When you get a surprisingly low price on a product do you assume that you got a really good deal or that you bought a low-quality product? Research indicates that you are more likely to associate low
Masculine-themed words (such as competitive, independent, analyze, strong) are commonly used in job recruitment materials, especially for job advertisements in male-dominated areas (Gaucher, Friesen,
The stimulant Ritalin has been shown to increase attention span and improve academic performance in children with ADHD (Evans et al., 2001). To demonstrate the effectiveness of the drug, a researcher
College athletes, especially males, are often perceived as having very little interest in the academic side of their college experience. One common problem is class attendance. To address the problem
Callahan (2009) demonstrated that tai chi can significantly reduce symptoms for individuals with arthritis.Participants were 18 years old or older with doctordiagnosed arthritis. Self-reports of pain
Research results indicate that physically attractive people are also perceived as being more intelligent(Eagly, Ashmore, Makhijani, & Longo, 1991). As a demonstration of this phenomenon, a researcher
There is some evidence suggesting that you are likely to improve your test score if you rethink and change answers on a multiple-choice exam (Johnston, 1975).To examine this phenomenon, a teacher
In Example 8.1 (page 200) we discussed a research study by Guéguen and Jacob (2012) showing that waitresses received significantly larger tips when they were wearing red T-shirts compared to other
Solve the following problems.a. A repeated-measures study with a sample of n 5 16 participants produces a mean difference of MD 5 3 with a standard deviation of s 5 4.Use a two-tailed hypothesis test
Solve the following problems.a. A repeated-measures study with a sample of n 5 16 participants produces a mean difference of MD 5 4 with a standard deviation of s 5 8.Use a two-tailed hypothesis test
A sample of difference scores from a repeatedmeasures experiment has a mean of MD 5 3 with a standard deviation of s 5 4.a. If n 5 4, is this sample sufficient to reject the null hypothesis using a
Participants enter a research study with unique characteristics that produce different scores from one person to another. For an independent-measures study, these individual differences can cause
Swearing is a common, almost reflexive, response to pain. Whether you knock your shin into the edge of a coffee table or smash your thumb with a hammer, most of us respond with a streak of
The previous problem demonstrates that removing individual differences can substantially reduce variance and lower the standard error. However, this benefit only occurs if the individual differences
Nothing has changed. With a 5 .05, is there a significant difference between the two treatment conditions?b. Now assume that the data are from a repeatedmeasures study using the same sample of n 5 9
Explain the difference between a matched-subjects design and a repeated-measures design.
A researcher conducts an experiment comparing two treatment conditions with 10 scores in each treatment condition.a. If an independent-measures design is used, how many participants are needed for
A repeated-measures, a matched-subjects, and an independent-measures study all produce a t statistic with df 5 16.How many participants were used in each study?
Describe parametric and nonparametric hypothesis tests.
Describe the data (observed frequencies) for a chi-square test for goodness of t.
Describe the hypotheses for a chi-square test for goodness of t, explain how the expected frequencies are obtained, and nd the expected frequencies for a specic research example.
Dene the degrees of freedom for the chi-square test for goodness of t and locate the critical value for a specic alpha level in the chi-square distribution.
Conduct a chi-square test for goodness of t and report the results as they would appear in the scientic literature.

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