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essentials of statistics

Questions and Answers of Essentials Of Statistics

10. Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest
9. Problem 22 in Chapter 9 described a study reporting that a good sense of humor can have a significant effect on how people judge the attractiveness of a potential romantic partner. In the study,
8. Problem 12 in Chapter 9 described a study that examined the spotlight effect, which refers to people overestimating the extent to which others notice their appearance or behavior. In the study, n
7. A researcher obtains a sample of n = 25 asthma patients and measures the severity of each person’s symptoms before and after they complete a 3-week relaxation training course. On average, the
6. A researcher obtains a sample from an unknown population and computes a sample mean of M = 43 with a standard deviation of s = 6.a. If the sample has n = 16 scores, compute an 80%confidence
5. For the following studies, state whether estimation or hypothesis testing is required. Also, is an independentor a repeated-measures t statistic appropriate?a. A researcher would like to determine
4. A researcher has constructed an 80% confidence interval of 45 8, using a sample of n 25 scores.a. What would happen to the width of the interval if the researcher had used a larger sample
3. Explain the trade off between precision and confidence for interval estimates.
2. Explain why it would not be reasonable to use estimation after a hypothesis test for which the decision was “fail to reject H0.”
1. Explain how the purpose of estimation differs from the purpose of a hypothesis test.
23. A researcher studies the effect of a drug (MAO inhibitor) on the number of nightmares occurring in veterans with post-traumatic stress disorder (PTSD).A sample of PTSD clients records each
22. At the Olympic-level of competition, even the smallest factors can make the difference between winning and losing. For example, Pelton (1983) has shown that Olympic marksmen shoot much better if
21. Placing children in time out can be an effective form of punishment. Research suggests that this same technique can also be effective for adults (Chelonis, Bastilla, Brown, & Gardner, 2007). In
20. A researcher uses a matched-samples design to investigate whether single people who own pets are generally happier than singles without pets. A mood inventory questionnaire is administered to a
19. 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
18. One of the primary advantages of a repeated-measures design, compared to independent-measures, is that it reduces the overall variability by removing variance caused by individual differences.
17. A variety of research results suggest that visual images interfere with visual perception. In one study, Segal and Fusella (1970) had participants watch a screen, looking for brief presentations
16. A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each participant ate a fixed diet without any oatmeal for
15. The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of n 4 participants before and after they receive the treatment.a. Calculate the
14. Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidants in foods such as blueberries may
13. 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
12. How would you react to doing much worse on an exam than you expected? There is some evidence to suggest that most individuals believe that they can cope with this kind of problem better than
11. Strack, Martin, and Stepper (1988) reported that people rate cartoons as funnier when holding a pen in their teeth (which forced them to smile) than when holding a pen in their lips (which forced
10. Research has shown that losing even one night’s sleep can have a significant effect on performance of complex tasks such as problem solving (Linde &Bergstroem, 1992). To demonstrate this
9. As mentioned in Chapters 2 and 3 (pages 56 and 67), Steven Schmidt (1994) reported a series of studies examining the effect of humor on memory. In one part of the study, participants were
8. A sample of difference scores from a repeatedmeasures experiment has a mean of MD 5 with a variance of s 2 64.a. If n 4, is this sample sufficient to reject the null hypothesis using a two-tailed
7.a. A repeated-measures study with a sample of n 9 participants produces a mean difference of MD 3 with a standard deviation of s 6. Based on the mean and standard deviation you should be able to
6.a. A repeated-measures study with a sample of n 9 participants produces a mean difference of MD 4 with a standard deviation of s 12. Based on the mean and standard deviation you should be able to
5. A sample of n 16 individuals participates in a repeated-measures study that produces a sample mean difference of MD 9 with SS 960 for the difference scores.a. Calculate the standard deviation for
4. A researcher conducts an experiment comparing two treatment conditions and obtains data with 10 scores for each treatment condition.a. If the researcher used an independent-measures design, how
3. Explain the difference between a matched-subjects design and a repeated-measures design.
2. 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
1. For the following studies, indicate whether a repeated-measures t test is the appropriate analysis.Explain your answers.a. A researcher is comparing the amount of time spent playing video games
23. Siegel (1990) found that elderly people who owned dogs were less likely to pay visits to their doctors after upsetting events than were those who did not own pets. Similarly, consider the
22. Steven Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were given a mix of humorous and nonhumorous sentences and
21. When people learn a new task, their performance usually improves when they are tested the next day, but only if they get at least 6 hours of sleep (Stickgold, Whidbee, Schirmer, Patel, & Hobson,
20. A researcher is comparing the effectiveness of two sets of instructions for assembling a child’s bike. A sample of eight fathers is obtained. Half of the fathers are given one set of
19. Research indicates that adolescent boys report higher levels of self-esteem than is reported by adolescent girls (Kling, Hyde, Showers, & Buswell, 1999). To examine this phenomenon a researcher
18. In 1974, Loftus and Palmer conducted a classic study demonstrating how the language used to ask a question can influence eyewitness memory. In the study, college students watched a film of an
17. Functional foods are those containing nutritional supplements in addition to natural nutrients. Examples include orange juice with calcium and eggs with omega-3. Kolodinsky, et al. (2008)
16. In a study examining overweight and obese college football players, Mathews and Wagner (2008) found that on average both offensive and defensive linemen exceeded the at-risk criterion for body
15. Do you view a chocolate bar as delicious or as fattening? Your attitude may depend on your gender.In a study of American college students, Rozin, Bauer, and Catanese (2003) examined the
14. A researcher conducts an independent-measures study comparing two treatments and reports the t statistic as t(30) = 2.085.a. How many individuals participated in the entire study?b. Using a
13. Suppose the research study in the previous problem produced larger variances of s 2 27 and s 2 21 for the two samples. Assuming that the means and sample sizes are the same as in problem 12,
12. An independent-measures research study was used to compare two treatment conditions with n 12 participants in each treatment. The first treatment had a mean of M 55 with a variance of s 2
11. For each of the following, assume that the two samples are selected from populations with equal means and calculate how much difference should be expected, on average, between the two sample
10. Two separate samples receive two different treatments.The first sample has n 9 with SS 710, and the second has n 6 with SS 460.a. Compute the pooled variance for the two samples.b.
9. Two separate samples, each with n 12 individuals, receive two different treatments. After treatment, the first sample has SS 1740 and the second has SS 1560.a. Find the pooled variance for
8. As noted on page 281, when the two population means are equal, the estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two
7. One sample has SS 70 and a second sample has SS 42.a. If n 8 for both samples, find each of the sample variances, and calculate the pooled variance.Because the samples are the same size, you
6. One sample has SS 48 and a second sample has SS 32.a. If n 5 for both samples, find each of the sample variances and compute the pooled variance. Because the samples are the same size, you
5. Describe the homogeneity of variance assumption and explain why it is important for the independentmeasures t test.
4. If other factors are held constant, how does increasing the sample variance affect the value of the independent-measures t statistic and the likelihood of rejecting the null hypothesis?
3. If other factors are held constant, how does increasing the number of scores in each sample affect the value of the independent-measures t statistic and the likelihood of rejecting the null
2. Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic.
1. Describe the basic characteristics of an independentmeasures, or a between-subjects, research study.
3. Brunt, Rhee, and Zhong (2008) surveyed 557 undergraduate college students to examine their weight status, health behaviors, and diet. Using body mass index(BMI), they classified the students into
2. A survey of female high school seniors shows that the average amount of time spent on clothes, hair, and makeup each morning before school is 35 minutes.Assume that the distribution of preparation
1. Find each of the requested values for a population with a mean of 40 and a standard deviation of 8.a. What is the z-score corresponding to X 52?b. What is the X value corresponding to z
23. A researcher expects a treatment to increase scores by 5 points. The regular population, without treatment, averages 40 with a standard deviation of 8, and the scores form a normal
22. A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of 80 and a standard deviation of 20. The researcher expects a
21. A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140. For this population, systolic scores
20. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant.a. Increasing the alpha level from .01 to .05.b. Changing from a
19. Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant.a. The size of the z-score in a hypothesis test.b. The size of
18. Researchers have often noted increases in violent crimes when it is very hot. In fact, Reifman, Larrick, and Fein (1991) noted that this relationship even extends to baseball. That is, there is a
17. Montarello and Martins (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further
16. A researcher is testing the hypothesis that consuming a sports drink during exercise improves endurance. A sample of n 50 male college students is obtained and each student is given a series of
15. A psychologist is investigating the hypothesis that children who grow up as the only child in the household develop different personality characteristics than those who grow up in larger
14. There is some evidence indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman, 2008). In a similar study, a
13. There is some evidence that REM sleep, associated with dreaming, may also play a role in learning and memory processing. For example, Smith and Lapp (1991) found increased REM activity for
12. A random sample is selected from a normal population with a mean of 40 and a standard deviation of 10.After a treatment is administered to the individuals in the sample, the sample mean is
11. 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,
10. A random sample of n 36 scores is selected from a normal population with a mean of 60. After a treatment is administered to the individuals in the sample, the sample mean is found to be M 52.a.
9. A random sample is selected from a normal population with a mean of 50 and a standard deviation of ?
8. State College is evaluating a new English composition course for freshmen. A random sample of n 25 freshmen is obtained and the students are placed in the course during their first semester. One
7. Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). In a
6. A researcher is investigating the effectiveness of a new study-skills training program for elementary school children. A sample of n 25 third-grade children is selected to participate in the
5. Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by
4. If the alpha level is changed from .05 to .01,a. What happens to the boundaries for the critical region?b. What happens to the probability of a Type I error?
3. In words, define the alpha level and the critical region for a hypothesis test.
2. The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the
1. In the z-score formula as it is used in a hypothesis test,a. Explain what is measured by M in the numerator.b. Explain what is measured by the standard error in the denominator.
22. Welsh, Davis, Burke, and Williams (2002)conducted a study to evaluate the effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance. Experienced athletes were given
21. People are selected to serve on juries by randomly picking names from the list of registered voters. The average age for registered voters in the county is 44.3 years with a standard deviation
20. The average age for licensed drivers in the county is 40.3 years with a standard deviation of 13.2 years.a. A researcher obtained a random sample of n 16 parking tickets and computed an
19. The machinery at a food-packing plant is able to put exactly 12 ounces of juice in every bottle. However, some items such as apples come in variable sizes so it is almost impossible to get
18. The population of SAT scores forms a normal distribution with a mean of 500 and a standard deviation of 100. If the average SAT score is calculated for a sample of n 25 students,a. What is
17. A population of scores forms a normal distribution with a mean of 80 and a standard deviation of 10.a. What proportion of the scores have values between 75 and 85?b. For samples of n 4, what
16. A population of scores forms a normal distribution with a mean of 40 and a standard deviation of 12.a. What is the probability of randomly selecting a score less than X 34?b. What is the
15. A population of scores forms a normal distribution with a mean of 75 and a standard deviation of 20.a. What proportion of the scores in the population have values less than X 80?b. If samples
14. The population of IQ scores forms a normal distribution with a mean of 100 and a standard deviation of 15. What is the probability of obtaining a sample mean greater than M 105,a. for a
13. A random sample is obtained from a normal population with a mean of 30 and a standard deviation of 8. The sample mean is M 33.a. Is this a fairly typical sample mean or an extreme value for a
12. A population forms a normal distribution with a mean of 80 and a standard deviation of 15. For each of the following samples, compute the z-score for the sample mean and determine whether the
11. A sample of n 25 scores has a mean of M 84.Find the z-score for this sample:a. If it was obtained from a population with 80 and 10.b. If it was obtained from a population with 80 and
10. For a population with a mean of 60 and a standard deviation of 24, find the z-score corresponding to each of the following samples.a. M 63 for a sample of n 16 scoresb. M 63 for a sample of n
9. For a sample of n 16 scores, what is the value of the population standard deviation () necessary to have a standard error ofa. M 10 points?b. M 5 points?c. M 2 points?
8. If the population standard deviation is 8, how large a sample is necessary to have a standard error that isa. less than 4 points?b. less than 2 points?c. less than 1 point?
7. For a population with a standard deviation of 10, how large a sample is necessary to have a standard error that is:a. less than or equal to 5 points?b. less than or equal to 2 points?c. less
6. For a population with a mean of 50 and a standard deviation of 10, how much error, on average, would you expect between the sample mean(M) and the population mean for:a. a sample of n 4
5. A population has a standard deviation of 30.a. On average, how much difference should exist between the population mean and the sample mean for n 4 scores randomly selected from the

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