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Statistics For The Behavioral Sciences 2nd Edition Susan A. Nolan, Thomas Heinzen - Solutions

Calculate degrees of freedom and identify the critical t value in each of the following circumstances:a. A two-tailed test based on 8 observations at a p level of 0.10b. A one-tailed test based on 42 observations at a p level of 0.05c. A two-tailed test based on 89 observations at a p level of 0.01
Identify the critical t value in each of the following circumstances:a. A one-tailed test with 73 degrees of freedom at a p level of 0.10b. A two-tailed test with 108 degrees of freedom at a p level of 0.05c. A one-tailed test with 38 degrees of freedom at a p level of 0.01
Calculate the t statistic for the data presented in Exercise 9.14, assuming l 0.96. Again, the data are 1.01, 0.99, 1.12, 1.27, 0.82, 1.04.
Calculate the t statistic for the data presented in Exercise 9.13, assuming l 96. Again, the data are 93, 97, 91, 88, 103, 94, 97.
using symbolic notation: 1.01, 0.99, 1.12, 1.27, 0.82, 1.04.
using symbolic notation: 93, 97, 91, 88, 103, 94, 97.
Calculate the standard error for t for the sample used in Exercise
For the data 1.01, 0.99, 1.12, 1.27, 0.82, 1.04, calculate the standard deviation under both of these conditions. (Note: You will have to carry some calculations out to the third decimal place to see the difference in calculations.)
For the data 93, 97, 91, 88, 103, 94, 97, calculate the standard deviation under both of these conditions:a. For the sampleb. As an estimate of the population
We use formulas to describe calculations. Find the error in symbolic notation in each of the following formulas.Explain why it is incorrect and provide the correct symbolic notation.a.b. X z(r) lM c.d.
What information does a dot plot provide?Calculating the Statistics
Explain what each part of the following statistic means, as it would be reported in APA format: t(4) 2.87, p 0.032.
Why do the t distributions merge with the z distribution as sample size increases?
How is the critical t value affected by sample size and degrees of freedom?
What does the phrase free to vary, referring to a number of scores in a given sample, mean for statisticians?
When is it appropriate to use a single-sample t test?
Define the symbols in the formula for the t statistic:
Explain why the standard error for the distribution of sample means is smaller than the standard deviation of sample scores.
How is the calculation of standard error different for a t test than for a z test?
Why do we modify the formula for calculating standard deviation when using t tests (and divide by N 1)?
When should we use a t distribution?
The research paper on culturally targeted therapy describe in Exercise 8.65 reported the following:Across all 76 studies, the random effects weighted average effect size was d .45 (SE .04, p .0001), with a 95% confidence interval of d .36 to d .53. The data consisted of 72 nonzero effect
A meta-analysis examined studies that compared two types of mental health treatments for ethnic and ra -cial minorities—the standard available treatments and treatments that were adapted to the clients’ cultures(Griner & Smith, 2006). An excerpt from the abstract follows:Many previous authors
In several exercises in this chapter, we considered the study of week 11 of the fall 2006 college football season, during which the population of 53 Division I-A games had a mean spread (winning score minus losing score)of 16.189, with a standard deviation of 12.128. The sample of four games that
The easiest way to increase statistical power is to increase sample size. Similarly, statistical power decreases with a smaller sample size. Use the data in Exercises 8.40 and 8.62 to answer the following:a. Compute the statistical power of the one-tailed statistical test with alpha of 0.05 when N
The easiest way to affect the outcome of a hypothesis test is to increase sample size. Similarly, true results may sometimes be missed because a sufficient sample was not used in the research.a. Perform the hypothesis test on the data in Exercise 8.40 with the sample of 37.b. Perform the same
Use the data presented in Exercise 8.40 to answer these questions:a. Without performing any computations, describe how statistical power is affected by performing a two-tailed test.b. Why are two-tailed tests recommended over onetailed tests?
We can witness the importance of alpha by recomputing statistical power for the data presented in Exercise 8.40.a. For this new computation, use alpha of 0.01, or 1%, for the one-tailed test.b. Explain why changing alpha affects power.c. If using a small
Calculate statistical power for the test performed in Exercise 8.56 using the following alpha levels in a onetailed test:a. alpha of 0.05, or 5%b. alpha of 0.10, or 10%c. Explain how power is affected by alpha in these calculations.
In Exercise 8.47, we explored a study of the Graded Naming Test.a. In Chapter 7, we calculated a z statistic of 4.97 for 30 participants. Determine prep for this example.(Note: Excel won’t work with a proportion of 0.0000, so use a proportion of 0.000001, a number very close to 0, instead.)b. In
Let’s assume the average speed of a serve in women’s tennis is around 118 mph, with a standard deviation of 12 mph. We recruit 26 amateur tennis players to use our method this time, and after six months we calculate a group mean of 123 mph.a. Using a 95% confidence interval, test the hypothesis
Let’s assume the average speed of a serve in men’s tennis is around 135 mph with a standard deviation of 6.5 mph. Because these statistics are calculated over many years and many players, we will treat them as population parameters. We develop a new training method that will increase arm
According to the Nielsen Company, Americans spend$345 million on chocolate during the week of Valentine’s Day. Let’s assume that we know the average married person spends $45 with a population standard deviation of $16. In February 2009, the U.S. economy was in the throes of a recession.
In Exercises 8.51 and 8.52, we considered the study of week 11 of the fall 2006 college football season. In an exercise in Chapter 7, we conducted a two-tailed hypothesis test and calculated a z statistic of 1.23.a. Determine prep for this example.b. Explain in your own words what this means.
In Exercises 8.51 and 8.52, we considered the study of week 11 of the fall 2006 college football season, during which the population of 53 Division I-A games had a mean spread (winning score minus losing score) of 16.189, with a standard deviation of 12.128. The sample of four games that were
Using the football data presented in Exercise 8.51, practice evaluating data using confidence intervals.a. Compute the 80% confidence interval.b. How do your conclusion and the confidence interval change as you move from 95% confidence to 80% confidence?c. Why don’t we talk about having 100%
In an exercise in Chapter 7, we asked whether college football teams tend to be more likely or less likely to be mismatched in the upper National Collegiate Athletic Association (NCAA) divisions. During week 11 of the fall 2006 college football season, the population of 53 Division I-A games had a
Your roommate is reading Fantasyland: A Season on Baseball’s Lunatic Fringe (Walker, 2006) and is intrigued by the statistical methods used by competitors in fantasy baseball leagues (in which competitors select their own team of baseball players from across all major league teams, winning in the
A Midwestern U.S. university reported that its social science majors tended to outperform its humanities majors on the LSATs (which gives them an edge at getting into law school). Sadie, an English major, and Kofi, a sociology major, both just took the LSAT.a. Can we tell which student will do
Unsavory researchers know that one can cheat with hypothesis testing. That is, they know that a researcher can stack the deck in her or his favor, making it easier to reject the null hypothesis.a. If you wanted to make it easier to reject the null hypothesis, what are three specific things you
In an exercise in Chapter 7, we asked you to conduct a z test to ascertain whether the Graded Naming Test(GNT) scores for Canadian participants differed from the GNT norms based on adults in England. The mean for a sample of 30 adults in Canada was 17.5. The normative mean for adults in England is
Here are summary data from a z test regarding scores on the Consideration of Future Consequences scale(Petrocelli, 2003): the population mean (l) is 3.51 and the population standard deviation (r) is 0.61. Imagine that a sample of 45 students had a mean of 3.7.a. Calculate the test statistic for a
A friend reads in her Introduction to Psychology textbook about a minority group in Japan, the Burakumin, who are racially the same as other Japanese people but are viewed as outcasts because their ancestors were employed in positions that involved the handling of dead animals (e.g., butchers). In
Assume you are conducting a meta-analysis over a set of five studies. The effect sizes for each study follows: d 0.67; d 0.03; d 0.32; d 0.59; d 0.22.a. Calculate the mean effect size for these studies.b. Use Cohen’s conventions to describe the mean effect size you calculated in part
Use Cohen’s conventions to describe the average effect size of d 0.11.
A meta-analysis reports an average effect size of d 0.11, with a confidence interval of d 0.08 to d 0.14. Would a hypothesis test (assessing the null hypothesis that the average effect size is 0) lead us to reject the null hypothesis? Explain.
A meta-analysis reports an average effect size of d 0.11, with a confidence interval of d 0.06 to d 0.28. Would a hypothesis test (assessing the null hypothesis that the average effect size is 0) lead us to reject the null hypothesis? Explain.
Using the table of numbers provided below, calculate statistical power for a one-tailed test (a 0.05, or 5%)aimed at determining if those in the sample sleep fewer hours, on average, than those in the population.
as a two-tailed test, determine prep.a. 2.23b. 1.82c. 0.33
as a onetailed test, determine prep. Be sure to use the appropriate p values.a. 2.23b. 1.82c. 0.33
The second step in calculating prep is conducted using software such as Microsoft Excel. For each of the three z statistics you considered in Exercise
For each of the following z statistics, calculate the p value for a two-tailed test.a. 2.23b. 1.82c. 0.33
The first step in calculating prep is knowing the actual p value of the test statistic. For each of the follow ing z statistics, calculate the p value for a one-tailed test.a. 2.23b. 1.82c. 0.33
For each of the following d values, identify the size of the effect using Cohen’s guidelines.a. d 0.79b. d 0.43c. d 0.22d. d 0.04
For each of the effect-size calculations in Exercise 8.33, identify the size of the effect using Cohen’s guidelines. Remember, for SAT math, l 500 and r 100.a. 61 people sampled have a mean of 480b. 82 people sampled have a mean of 520c. 6 people sampled have a mean of 610
Calculate the effect size for each of the following average SAT math scores. Remember, SAT math is standardized such that l 500 and r 100.a. 61 people sampled have a mean of 480b. 82 people sampled have a mean of 520c. 6 people sampled have a mean of 610
Calculate the effect size for the mean of 1057 observed in Exercise 8.31 where l 1014 and r 136.
For a given variable, imagine we know that the population mean is 1014 and the standard deviation is 136.A mean of 1057 is obtained based on sampling. Calculate the z test statistic for this mean, assuming it was found using each of the following sample sizes:a. 12b. 39c. 188
Calculate the standard error for each of the following sample sizes when l 1014 and r 136:a. 12b. 39c. 188
Calculate the 99% confidence interval for the same fictional data regarding daily TV viewing habits: l 4.7 hours; r 1.3 hours; sample of 78 people with mean of 4.1 hours.
Calculate the 80% confidence interval for the same fictional data regarding daily TV viewing habits: l 4.7 hours; r 1.3 hours; sample of 78 people with mean of 4.1 hours.
Calculate the 95% confidence interval for the following fictional data regarding daily TV viewing habits: l 4.7 hours; r 1.3 hours; sample of 78 people with a mean of 4.1 hours.
For each of the following confidence intervals, look up the critical z values for a two-tailed test.a. 80%b. 85%c. 99%
For each of the following confidence intervals, look up the critical z value for a one-tailed test.a. 80%b. 85%c. 99%
For each of the following confidence intervals, indicate how much of the distribution would be placed in the cutoff region for a two-tailed test.a. 80%b. 85%c. 99%
For each of the following confidence intervals, indicate how much of the distribution would be placed in the cutoff region for a one-tailed test.a. 80%b. 85%c. 99%
In 2006, approximately 47% of Americans, when surveyed by a Gallup poll, felt that having a gun in the home made them safer than having no gun. The margin of error reported was 3%. Construct an interval estimate.
In 2008, 22% of Gallup respondents indicated suspicion of steroid use by athletes who broke world records in swimming. Calculate an interval estimate using a margin of error at 3.5%.
In 2008, the Gallup poll asked people whether or not they were suspicious of steroid use among Olympic athletes. Thirty-five percent of respondents indicated suspicion when they saw an athlete break a track-and-field record, with a 4% margin of error. Calculate an interval estimate.
In statistics, concepts are often expressed in symbols and equations. For each of the following, (i) identify the incorrect symbol, (ii) state what the correct symbol should be, and (iii) explain why the initial symbol was incorrect.a. Mlower z(r) Msample b.
Why is it important for a researcher who is conducting a meta-analysis to find not only published studies but also unpublished studies?
What is the goal of a meta-analysis?
How are statistical power and effect size different but related?
List the five factors that affect statistical power. For each, indicate how a researcher can leverage that factor to increase power.
Explain how increasing alpha increases statistical power.
Traditionally, what minimum percentage chance of correctly rejecting the null hypothesis do we need in order to proceed with an experiment?
How does statistical power relate to Type II errors?
In your own words, define the word power—first as you would use it in everyday conversation and then as a statistician would use it.
Why is it useful to calculate prep in addition to, or instead of, a p value?
What are Cohen’s guidelines for small, medium, and large effects?
What does it mean to say the effect-size statistic, such as Cohen’sd, neutralizes the influence of sample size?
Relate effect size to the concept of overlap between comparison distributions.
What effect does increasing the sample size have on the standard error and the test statistic for every hypothesis test?
In your own words, define the word effect—first as you would use it in everyday conversation and then as a statistician would use it.
What are the five steps to create a confidence interval for a z distribution?
Why do we calculate confidence intervals?
In your own words, define the word confidence—first as you would use it in everyday conversation and then as a statistician would use it in the context of a confidence interval.
What specific danger exists when reporting a statistically significant difference between two group means?
In Next Steps: Cleaning Data, we noted that the z distribution is sometimes used to identify potential outliers in a data set. www.boxofficemojo.com provides data on U.S. box office receipts for major films. Here are domestic box office grosses for a randomly selected sample of 15 of the 100
You have conducted a study with 120 participants(60 female, 60 male) about the relation between attitudes toward cohabitation prior to marriage (on a 30-item scale) and self-reported sexual behaviors (on a 20-item scale). Most respondents filled out both scales completely. Everyone completed the
You have just conducted a study testing how well two independent variables, daily sugar intake (as assessed by a 25-item eating habits scale) and physical activity (as assessed by a 20-item daily physical activity scale), predicted the dependent variable of blood sugar levels.There were only 17
A recent research report (Behenam & Pooya, 2006)began, “There is probably no other area of health care that requires a cooperation to the extent that orthodontics does,” and explored factors that affected the number of hours per day that Iranian patients wore their orthodontic appliances. The
When we change the p level that we use as a cutoff, there is a small change in step 4 of hypothesis testing.Although 0.05 is the most commonly used p level, other values, such as 0.01, are often used. Let’s consider Exercise 7.50 on the Graded Naming Test.a. Conduct step 4 of hypothesis testing
When we conduct a one-tailed test instead of a twotailed test, there are small changes in steps 2 and 4 of hypothesis testing. Let’s consider Exercise 7.50 on the Graded Naming Test. (Note: For this example, assume that those from populations other than the one on which it was normed will score
z tests are often used when a researcher wants to compare his or her sample to known population norms.The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test, often used to detect brain damage, starts with easy words like kangaroo and gets
Refer to Exercise 7.47. The results for the four Division I-AA Patriot League games are as follows:Holy Cross, 27/Bucknell, 10 Lehigh, 23/Colgate, 15 Lafayette, 31/Fordham, 24 Georgetown, 24/Mar ist, 21a. Conduct steps 3 through 6 of hypothesis testing.[You already conducted steps 1 and 2 in
Refer to Exercise 7.47.a. State the null hypothesis and the research hypothesis for a two-tailed test in both words and symbols.b. One of our students hypothesized that the spread would be bigger among the Division I-AA teams because “some of them are really bad and would get trounced.” State
Let’s consider whether U.S. college football teams are more likely or less likely to be mismatched in the upper National Collegiate Athletic Association(NCAA) divisions. The highest division, Division I(technically, Division I-A), includes such vaunted teams as the Ohio State University Buckeyes
Refer to the scenario described in Exercise 7.45.a. State the null and research hypotheses for a twotailed test in both words and symbols.b. Imagine that, based on these findings, you wanted to replicate this study. Based on the findings described in Exercise 7.45, state the null and research
Boone (1992) examined scores on the Wechsler Adult Intelligence Scale–Revised (WAIS-R) for 150 adult psychiatric inpatients. He determined the “intrasubtest scatter” score for each inpatient. Intrasubtest scatter refers to patterns of responses in which respondents are almost as likely to get

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