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essentials of statistics

Questions and Answers of Essentials Of Statistics

Explain why t distributions tend to be flatter and more spread out than the normal distribution.
Find the t values that form the boundaries of the critical region for a two-tailed test with a 5 .05 for each of the following sample sizes:a. n 5 4b. n 5 15c. n 5 24
Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailed test with a 5 .01 for each of the following sample sizes.a. n 5 10b. n 5 20c. n 5 30
A random sample of n 5 12 individuals is selected from a population with m 5 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M 5
A random sample of n 5 4 individuals is selected from a population with m 5 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M 5
Infants, even newborns, prefer to look at attractive faces compared to less attractive faces (Slater, et al., 1998). In the study, infants from 1 to 6 days old were shown two photographs of women’s
The spotlight effect refers to overestimating the extent to which others notice your appearance or behavior, especially when you commit a social faux pas.Effectively, you feel as if you are suddenly
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of m 5 40, and the treatment is administered to the individuals in the sample. After treatment, the sample
To evaluate the effect of a treatment, a sample of n 5 6 is obtained from a population with a mean of m 5 80, and the treatment is administered to the individuals in the sample. After treatment, the
Weinstein, McDermott, and Roediger (2010) report that students who were given questions to be answered while studying new material had better scores when tested on the material compared to students
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of m 5 20, and the treatment is administered to the individuals in the sample. After treatment, the sample
To evaluate the effect of a treatment, a sample of n 5 8 is obtained from a population with a mean of m 5 50, and the treatment is administered to the individuals in the sample. After treatment, the
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 Anxiety
Ackerman and Goldsmith (2011) found that students who studied text from printed hardcopy had better test scores than students who studied from text presented on a screen. In a related study, a
Oishi and Shigehiro (2010) report that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. To further examine this relationship, a
McGee and Shevlin (2009) demonstrated that an individual’s sense of humor had a significant effect on how the individual was perceived by others. In one part of the study, female college students
Belsky, Weinraub, Owen, and Kelly (2001) reported on the effects of preschool child care on the development of young children. One result suggests that children who spend more time away from their
An example of the vertical-horizontal illusion is shown in the figure. Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength of this
Dene independent-measures designs and repeated-measures designs and identify examples of each.
Describe the hypotheses for an independent-measures t test.
Describe the structure of the independent-measures t statistic and explain how it is related to the single-sample t.
Calculate the pooled variance for two samples and the estimated standard error for the sample mean difference, and explain what each one measures.
Calculate the complete independent-measures t statistic and its degrees of freedom.
Use the data from two samples to conduct an independent-measures t test evaluating the signicance of the difference between two population means.
Conduct a directional (one-tailed) hypothesis test using the independent-measures t statistic.
Describe the basic assumptions underlying the independent-measures t hypothesis test, especially the homogeneity of variance assumption, and explain how the homogeneity assumption can be tested.
Measure effect size for an independent-measures t test using either Cohen’s d or r2, the percentage of variance accounted for.
Use the data from two separate samples to compute a condence interval describing the size of the mean difference between two treatment conditions or two populations.
Describe the relationship between a hypothesis test with an independent-measures t statistic using a 5 .05 and the corresponding 95% condence interval for the mean difference.
Describe how the results of an independent-measures t test and measures of effect size are reported in the scientic literature.
Describe how sample size and sample variance inuence the outcome of a hypothesis test and measures of effect size for the independent-measures t statistic.
Which of the following is most likely to be an independent-measures design?a. A study comparing self-esteem for children from single-parent homes and children from two-parent homesb. A study
Which of the following is most likely to be a repeated-measures design?a. A study comparing motor-skills performance for left-handed adolescents and right-handed adolescentsb. A study comparing
An independent-measures study comparing two treatment conditions uses _____________ groups of participants and obtains _____________ score(s) for each participant.a. 1, 1b. 1, 2c. 2, 1d. 2, 2
Which of the following is the correct null hypothesis for an independentmeasures t test?a. There is no difference between the two sample means.b. There is no difference between the two population
Which of the following does not accurately describe the relationship between the formulas for the single-sample t and the independent-measures t?a. The single-sample t has one sample mean and the
One sample has n 5 4 and a second sample has n 5 8.If the pooled variance for the two samples is 24, then what is the estimated standard error for the sample mean difference?a. 9b. 4c. 3d. 2
A researcher obtains M 5 34 with SS 5 190 for a sample of n 5 10 girls and M 5 29 with SS 5 170 for a sample of n 5 10 boys. If the two samples are used to evaluate the mean difference between the
What is the value of the independent-measures t statistic for a study with n 5 10 participants in each treatment if the data produce M 5 38 and SS 5 200 for the first treatment and M 5 33 and SS 5
A researcher uses two samples, each with n 5 15 participants, to evaluate the mean difference in performance scores between 8-year-old and 10-year-old children. The prediction is that the older
Hartley’s F-max test is used to evaluate the homogeneity of variance assumption. What is the null hypothesis for this test?a. The two sample variances are equal.b. The two sample variances are not
A researcher obtains a mean of M 5 26 for a sample in one treatment condition and M 5 28 for a sample in another treatment. The pooled variance for the two samples is 16.What value would be obtained
Which of the following is not an accurate description of a confidence interval for a mean difference using the independent-measures t statistic?a. The sample mean difference, M1 2 M2, will be located
Which of the following accurately describes the 95% confidence interval for an independent-measures study for which a hypothesis test concludes that there is no significant mean difference with a 5
The results of a hypothesis test with an independent-measures t statistic are reported as follows: t(22) 5 2.48, p , .05, d 5 0.27. Which of the following is an accurate description of the study and
Which of the following accurately describes how the outcome of a hypothesis test and measures of effect size with the independent-measures t statistic are affected when sample size is increased?a.
Which of the following accurately describes how the outcome of a hypothesis test and measures of effect size with the independent-measures t statistic are affected when sample variance increases?a.
Which of the following sets of data would produce the largest value for an independent-measures t statistic?a. Two sample means of 10 and 12 with sample variances of 20 and 25b. Two sample means of
Describe the basic characteristics that define an independent-measures, or a between-subjects, research study.
Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic.
One sample has SS 5 36 and a second sample has SS 5 24.a. If n 5 5 for both samples, find each of the sample variances and compute the pooled variance. Because the samples are the same size, you
One sample has SS 5 60 and a second sample has SS 5 48.a. If n 5 7 for both samples, find each of the sample variances, and calculate the pooled variance.Because the samples are the same size, you
Two separate samples, each with n 5 9 individuals, receive different treatments. After treatment, the first sample has SS 5 546 and the second has SS 5 606.a. Find the pooled variance for the two
Two separate samples receive different treatments.After treatment, the first sample has n 5 6 with SS 5 236, and the second has n 5 12 with SS 5 340.a. Compute the pooled variance for the two
Research results suggest a relationship between the TV viewing habits of 5-year-old children and their future performance in high school. For example, Anderson, Huston, Wright, and Collins (1998)
Does posting calorie content for menu items affect people’s choices in fast-food restaurants? According to results obtained by Elbel, Gyamfi, and Kersh(2011), the answer is no. The researchers
A long history of psychology research has demonstrated that memory is usually improved by studying material on multiple occasions rather than one time only. This effect is commonly known as
Recent research has shown that creative people are more likely to cheat than their less-creative counterparts (Gino & Ariely, 2011). Participants in the study first completed creativity assessment
Recent research has demonstrated that music-based physical training for elderly people can improve balance, walking efficiency, and reduce the risk of falls (Trombetti et al., 2011). As part of the
McAllister et al. (2012) compared varsity football and hockey players with varsity athletes from noncontact sports to determine whether exposure to head impacts during one season have an effect on
Zhou and Vohs (2009) published a study showing that handling money reduces the perception pain.In the experiment, a group of college students was told that they were participating in a manual
In a classic study in the area of problem solving, Katona (1940) compared the effectiveness of two methods of instruction. One group of participants was shown the exact, step-by-step procedure for
A researcher conducts an independent-measures study comparing two treatments and reports the t statistic as t(18) 5 2.15.a. How many individuals participated in the entire study?b. Using a two-tailed
In a recent study, Piff, Kraus, Côté, Cheng, and Keltner (2010) found that people from lower socioeconomic classes tend to display greater prosocial behavior than their higher-class counterparts.
Describe the homogeneity of variance assumption and explain why it is important for the independentmeasures t test.
If other factors are held constant, explain how each of the following influences the value of the independentmeasures t statistic, the likelihood of rejecting the null hypothesis, and the magnitude
As noted on page 275, 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 sample
Two samples are selected from the same population.For each of the following, calculate how much difference is expected, on average, between the two sample means.a. One sample has n 5 4, the second
For each of the following, assume that the two samples are obtained from populations with the same mean, and calculate how much difference should be expected, on average, between the two sample
For each of the following, calculate the pooled variance and the estimated standard error for the sample mean differencea. The first sample has n 5 4 scores and a variance of s2 5 17, and the second
It appears that there is some truth to the old adage“That which doesn’t kill us makes us stronger.” Seery, Holman, and Silver (2010) found that individuals with some history of adversity report
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
Explain how a z-score identies a precise location in a distribution for either a population or a sample of scores.
Using either the z-score denition or the z-score formula, transform X values into z-scores and transform z-scores into X values for both populations and samples.
Explain how z-scores establish a relationship among X, the mean, the standard deviation, and the value of z, and use that relationship to nd an unknown mean when given a z-score, a score, and the
Describe the effects of standardizing a distribution by transforming the entire set of scores into z-scores and explain the advantages of this transformation.
Use z-scores to transform any distribution into a standardized distribution with a predetermined mean and a predetermined standard deviation.
Explain how z-scores can help researchers use the data from a sample to draw inferences about populations.
What location in a distribution corresponds to z 5 22.00?a. Above the mean by 2 pointsb. Above the mean by a distance equal to 2 standard deviationsc. Below the mean by 2 pointsd. Below the mean by a
For a population with m 5 80 and s 5 12, what is the z-score corresponding to X 5 92?a. 10.50b. 11.00c. 11.20d. 112.00
For a sample with M 5 72 and s 5 4, what is the X value corresponding to z 5 22.00?a. X 5 70b. X 5 68c. X 5 64d. X 5 60
In a population with m 5 60, a score of X 5 58 corresponds to a z-score of z 5 20.50. What is the population standard deviation?a. 1b. 2c. 4d. Cannot be determined without additional information
In a sample with a standard deviation of s 5 8, a score of X 5 64 corresponds to z 5 20.50. What is the sample mean?a. M 5 56b. M 5 60c. M 5 68d. M 5 72
In a population of scores, X 5 45 corresponds to z 5 12.00 and X 5 30 corresponds to z 5 21.00. What is the population mean?a. 30b. 35c. 37.5d. 40
In a sample, X 5 70 corresponds to z 5 12.00 and X 5 65 corresponds to z 5 11.00. What are the sample mean and standard deviation?a. M 5 60 and s 5 5b. M 5 60 and s 5 10c. M 5 50 and s 5 10d. M 5 50
A population with m 5 80 and s 5 15 is transformed into z-scores. After the transformation, what is the mean for the population of z-scores?a. m 5 80b. m 5 1.00c. m 5 0d. Cannot be determined from
A sample with a mean of M 5 50 and a standard deviation of s 5 12 is being transformed into z-scores. After the transformation, what is the standard deviation for the sample of z-scores?a. 0b. 1c. n
Which of the following is an advantage of transforming X values into z-scores?a. All negative numbers are eliminated.b. The distribution is transformed to a normal shape.c. All scores are moved
Last week Sarah had exams in math and in Spanish. On the math exam, the mean was m 5 30 with s 5 5, and Sarah had a score of X 5 45.On the Spanish exam, the mean was m 5 60 with s 5 6 and Sarah had a
A set of scores has a mean of m 5 63 and a standard deviation of s 58.If these scores are standardized so that the new distribution has m 5 50 and s 5 10, what new value would be obtained for a score
A distribution with m 5 35 and s 5 8 is being standardized so that the new mean and standard deviation will be m 5 50 and s 510.When the distribution is standardized, what value will be obtained for
Using z-scores, a sample with M 5 37 and s 5 6 is standardized so that the new mean is M 5 50 and s 510.How does an individual’s z-score in the new distribution compare with his/her z-score in the
For the past 20 years, the high temperature on April 15th has averaged m 5 62 degrees with a standard deviation of s 54.Last year, the high temperature was 72 degrees. Based on this information, last
A score of X 5 73 is obtained from a population. Which set of population parameters would make X 5 73 and extreme, unrepresentative score?a. m 5 65 and s 5 8b. m 5 65 and s 5 3c. m 5 70 and s 5 8d. m
Under what circumstances would a score that is 15 points above the mean be considered an extreme score?a. When the mean is much larger than 15b. When the standard deviation is much larger than 15c.
For a population with a standard deviation of s 5 20, find the z-score for each of the following locations in the distribution.a. Above the mean by 5 pointsb. Above the mean by 2 pointsc. Below the
For a sample with a standard deviation of s 5 12, describe the location of each of the following z-scores in terms of its position relative to the mean. For example, z 5 11.00 is a location that is
For a population with m 5 40 and s 5 8:a. Find the z-score for each of the following X values.(Note: You should be able to find these values using the definition of a z-score. You should not need to
For a population with m 5 80 and s 5 9, find the z-score for each of the following X values. (Note: You probably will need to use a formula and a calculator to find these values.)X 5 83 X 5 75 X 5 91
A sample has a mean of M 5 90 and a standard deviation of s 5 20.a. Find the z-score for each of the following X values.X 5 95 X 5 98 X 5 105 X 5 80 X 5 88 X 5 76b. Find the X value for each of the

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