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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
Explain how measures of effect size such as Cohen’s d are in uenced by the sample size and the standard deviation.
De ne the power of a hypothesis test and explain how power is related to the probability of a Type II error.
Identify the factors that in uence 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 inferential technique that uses the data from a sample to draw inferences about a populationd. 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 is the correct statement of the null hypothesis?a. m 5 60b. m ? 60c. M 5 60d. M ? 60
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 probability if the null hypothesis is truec. Outcomes that have a very low probability whether or not the
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 effect?a. The sample mean should be very different from 80 and should lead you to reject the null
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 concluded that a treatment has no effect.d. A researcher has correctly concluded that a treatment
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 hypothesis
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 likelihood of rejecting H0 and increase the risk of a Type I error.c. It will increase 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 rejected.b. The obtained sample mean was very likely if the null hypothesis is true, so H0 was rejected.c.
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 effect of increasing the sample size to n 5 25?a. Increase the chances that the sample will produce
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 obtained by random sampling.c. The scores in the sample are independent observations.d. The distribution
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 of the following is the correct statement of the null hypothesis?a. m $ 50b. m . 50c. m # 50d. m , 50
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 examined using a one-tailed hypothesis test. Which of the following is the correct statement of the
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. 11.65d. 62.33
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. With a small sample and a large standard deviationd. With a small sample and a small standard deviation
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 Cohen’s d and obtains d 5 0.25. What was the sample mean?a. M 5 81b. M 5 82c. M 5 83d. M 5 84
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 rejecting the null hypothesis and increases the value of Cohen’s d.b. A larger sample increases the
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 to power.d. It is impossible to determine without knowing the alpha level for the test.
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 power of the test.b. Increasing sample size decreases 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 both decrease power.c. A larger sample will increase power but a larger alpha will decrease power.d.
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 population standard deviationc. Increasing the number of scores in the sample
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 pages.To test this finding, a professor identifies a sample of n 5 16 students who used the electronic
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 determine whether this average has changed in recent years, a researcher selected a sample of n 5 64 of
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 representative study, a sample of n 5 100 adolescents with a history of group participation is given 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 registered for Introductory Psychology is placed in the online version of the course. At the end of
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 found to be M 5 37.a. If the sample consists of n 5 36 scores, is the sample mean sufficient to
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 54.a. If the population standard deviation is s 5 8, is the sample mean sufficient to conclude that the
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 study, female college students were given brief descriptions of a potential romantic partner and then
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 found to be M 5 46.a. How large a sample is necessary for this sample mean to be statistically
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 distribution with a mean of m 5 9.6 and a standard deviation of s 5 1.9. To see if the data showed
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 the year, each student takes the SAT. The average score for this sample is M 5 562.For the general
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, suppose that a researcher selects a random sample of n 5 36 male undergraduates and a sample of n 5 25
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 compared to very hot or very cold conditions. To verify this result, a researcher collected a
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 6-point treatment effect and plans to use a two-tailed hypothesis test with a 5 .05.a. Compute the
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 standardized dexterity task. The treatment is expected to lower scores on the test by an average of 30 points.
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 points per decade. To examine this effect, a researcher obtains an IQ test with instructions for scoring
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 (24)h. 26 3 (22) 3 (23)i. 212 4 (23)j. 18 4 (26)
De ne 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 signi cance 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 con dence 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 scienti c literature.
Describe how the outcome of a hypothesis test and measures of effect size using the repeated-measures t statistic are in uenced by sample size and sample variance.
Describe how the consistency of the treatment effect is re ected in the variability of the difference scores and explain how this in uences 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, evaluate the situations in which each design would be more appropriate.
De ne 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 researcher would like to study the effect of practice on performance.b. A researcher would like to
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 participated in the research study?a. 10b. 20c. 21d. 40
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 subject.a. 1, 1b. 1, 2c. 2, 1d. 2, 2
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 mean.c. Each uses one sample variance to compute the standard error.d. All of the above.
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 decision for a two-tailed test?a. Reject the null hypothesis with a 5 .05 but fail to reject with a 5
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 scores, then which of the following is the correct statement of the alternative hypothesis (H1)?a. uD $
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 of variance, r 2, is used to measure effect size, then what is the value of r 2?a. 9 33 5 0.27b. 3
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 of the interval and what t values are used to construct the interval?a. The sample mean difference
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 conclude about the outcome of the hypothesis test?a. The test rejected the null hypothesis.b. The
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 for the hypothesis test?a. A large sample size (n) and a large varianceb. A large sample size (n)
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 the data?a. The variance of the difference scores is small and the likelihood of a signi -cant
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 individual differences rather than treatment differencesd. All of the other options are major concerns.
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 treatment is likely to produce a permanent change in the participant’s performanceb. When
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 behavior by comparing aggressive behaviors for one group who just finished playing a violent game
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 experiment?b. If a repeated-measures design is used, how many subjects are needed for the experiment?
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 deviation for the sample of difference scores. Briefly explain what is measured by the standard deviation.b.
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 photograph with the tattoo removed. Suppose a similar experiment is conducted as a repeated-measures
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 difference scores and MD.b. Compute SS, sample variance, and estimated standard error.c. Is there a
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 price and low quality if someone else makes the purchase rather than yourself (Yan & Sengupta,
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, & Kay, 2010). The same study found that these words also make the jobs less appealing to women. In
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 selects a sample of n 5 20 children diagnosed with the disorder and measures each child’s
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 of class attendance, a group of researchers developed and demonstrated a relatively simple but
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 and stiffness were measured at the beginning of an eight-week tai chi course and again at the end.
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 obtained a set of 10 photographs, 5 showing men who were judged to be attractive and 5 showing men
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 gave the same final exam to two sections of a psychology course. The students in one section were told
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 colors. The actual study used a repeated-measures design in which waitresses in five different
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 with a 5 .05 to determine whether this sample provides evidence of a significant treatment
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