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probability statistics
Essential Statistics For The Behavioral Sciences 2nd Edition Gregory J Privitera - Solutions
A researcher measures the time it takes 13 men and 15 women to complete multiple tasks in a study. She compares the mean difference between men and women using the two-independent-sample t test. What is the critical value for this test if she conducts a two-tailed test at a .05 level of
What value is placed in the denominator for the two-independent-sample t test?
What are the four assumptions for the two-independent-sample t test?
Identify the assumptions for a two-independent-sample t test.
Describe the between-subjects design, and identify two appropriate sampling methods used to select independent samples.
The usefulness of confidence intervals. To clarify the kind of information conveyed by a level of confidence, Thompson (2007) stated, “CIs are extremely useful because they convey not only our point estimate, but also, via the width of the intervals, something about the precision of our
Using CIs for statistical inference. In an article contrasting hypothesis testing with the use of confidence intervals, Hoekstra, Johnson, and Kiers (2012) explained, “When a CI is used only to determine whether the null value lies within the interval, the statistical inference is no different
Assumptions for the one-sample t test. In a critical evaluation of the one-sample t test, Rochon and Kieser (2011) explained that “a one-sample t test is used when inference about the population mean μ is made for a sample of n independent observations” (p. 411). Identify the assumption for
Calculating a t test. In a review that, in part, reviewed t tests, Wall Emerson (2017) made the following two statements (p. 194):Statement 1: “The t statistic [is] calculated by taking the [mean] difference . . . and dividing that difference by the square root of a measure of variance which is
Estimating effect size. Yuan and Maxwell (2005) investigated how the power of a study influences the decisions researchers make in an experiment. In their introduction concerning effect size, they stated that “the exact true effect size is generally unknown even after the experiment. But one can
Controlling the alpha level. In an article evaluating the utility of t tests for biomedical research, Kreinovich and Servin (2015) explained that “for the t test, we estimate a statistic t. The hypothesis is confirmed, with given confidence α” (Kreinovich & Servin, 2015, p. 95). From this
Suppose a researcher has participants rate how much their mood improves following an exercise on a bipolar scale from −3 (much worse) to +3 (much improved), with the midpoint, 0, indicating no change in mood. If following the exercise the researcher reports a 95% CI =0.5 to 1.3, did she observe a
A researcher computes the following 95% CI = 12 to 24. What is the point estimate for this 95% CI?
Using Cohen’sd, state whether a 3-point treatment effect (M − μ = 3) is small, medium, or large for a one-sample t test, given the following values for the sample standard deviation:1. SD = 3 2. SD = 6 3. SD = 12 4. SD = 24
An instructor implements a new teaching strategy in the classroom by using a teaching strategy to teach a sample of six students. After the instruction, he gives each student a test out of 100 possible points to test their recall. The scores are listed in the table.1. Find the confidence limits at
Listening to music has long been thought to enhance intelligence, especially during infancy and childhood. To test whether this is true, a researcher records the number of hours that eight highperforming students listened to music per day for 1 week. The data are listed in the table.1. Find the
While researching lifestyle changes to improve heart health, you come across a research article reporting that the average American in the population consumes about 2,700 calories per day. You come across another article that refutes this, stating that a sample of Americans consumed significantly
A school psychologist notes that the average number of times that students are disruptive during class is 1.4 (μ = 1.4) times per day. Following recent classroom policy changes, the psychologist tests if the number of disruptions during class has changed. He records the following number of
A social psychologist notes that the average time a person spends on social media is 2 hours a day. The researcher wants to test whether new parents spend more or less time than 2 hours on social media. She records the following number of hours spent on social media in a sample of 15 new parents:
Researchers report a 95% CI = 1.56 to 5.77. What would the decision be for a hypothesis test if the null hypothesis were:1. μ = 0?2. μ = 3?3. μ = 6?
A researcher tests the null hypothesis that the mean intelligence score in the population of adult learners using the standard IQ test is μ = 100. In his sample, he identifies a 95% CI = 99.1 to 102.3. What would the decision have been for this test using the one-sample t test? Explain your answer.
State the total degrees of freedom for the following t tests:1. n = 12 for a one-sample t test 2. Critical value = 1.645 for a one-tailed test, α = .05
State the critical values for a one-sample t test given the following conditions:1. Two-tailed test, α = .05, n = 12 2. One-tailed test, lower-tail critical, α = .01, df = 15 3. Two-tailed test, α = .01, df = 26 4. One-tailed test, upper-tail critical, α = .05, n = 30
Will each of the following increase, decrease, or have no effect on the value of the test statistic in a one-sample t test?1. The sample variance is doubled.2. The level of significance is reduced from .05 to .01.3. The sample size is increased.4. The difference between the sample and population
The values listed below are the obtained values for a t statistic. (1) What is your decision for each if df = 30 and α = .05 for a two-tailed test? (2) What is your decision for each if df = 30, and we change to α = .01 for an upper-tail critical test?1. tobt = 2.050 2. tobt = 1.680 3. tobt =
In the following studies, state whether the one-sample t test is an appropriate test statistic to analyze data. If not, then explain why it is not appropriate.1. A study testing whether night-shift workers sleep the recommended 8 hours per day 2. A study measuring differences in attitudes about
What are the three steps to compute an estimation formula?
Who determines the level of confidence for an interval estimate?
Define point estimation and interval estimation.
Name two measures of proportion of variance for the one-sample t test. Which measure is the most conservative?
Name three measures used to estimate effect size for the one-sample t test.
Name the t test used in hypothesis testing to evaluate the mean observed in one sample.
Why are the degrees of freedom for the t distribution and the degrees of freedom for sample variance the same?
How does our estimate of the population variance change as the sample size increases? Explain.
The sample variance is used in the formula for standard error when the population variance is not known. Why is it appropriate to substitute the sample variance for the population variance?
What test is used as an alternative to the z test when the population variance is unknown?
A researcher notes that the null hypothesis of μ = 6 is not contained within the 95% confidence interval.Based on this result, would the decision have been to retain or reject the null hypothesis using hypothesis testing?
A researcher measures M = 3.406 and SD = 4.0 in one sample of 16 participants. What is the 95% CI(confidence interval) for these data using the estimation formula for a one-sample t test?
State the estimation formula for a one-sample t test.
What measure, eta-squared or omega-squared, gives a more conservative or smaller estimate of proportion of variance?
A researcher reports that a sample of workers with high-stress careers slept significantly less than workers in the general population, t(48) = 2.36, p < .05. Compute eta-squared for this one-sample t test.
State whether each of the following values for estimated Cohen’s d has a small, medium, or large effect size.1. 0.40 2. 1.20 3. 0.05 4. 0.10
A researcher compares the mean grade point average (GPA) of college students with a full-time job to the mean GPA of the general population of college students. In this example, identify (a) the dependent variable and (b) the treatment.
An estimated Cohen’s d substitutes which value in the formula to estimate the population standard deviation?
Using the same study described in Question 2 with α = .01, what is the decision if the following values for the test statistic are obtained?1. 2.558 2. 1.602 3. 2.999 4. −3.404
Researchers record the number of errors on some behavioral task for 15 participants. They report a sample mean equal to 6 ± 1 (M ± SD). What is the critical value for a two-tailed test with α = .01?
What are three assumptions of the one-sample t test?
Assuming α = .05, what is the critical value in each of the following t distributions?1. df = 10, two-tailed test 2. df = 30, one-tailed test (lower-tail critical)3. df = ∞, two-tailed test 4. df = 15, one-tailed test (upper-tail critical)
What are the degrees of freedom for each of the following samples?1. n = 12 2. n = 22 3. n = 5 4. n = 30
What is the calculation for the degrees of freedom of a t distribution?
How does increasing sample size affect the estimate of the population variance?
The __________________ is a normal-like distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance to estimate the standard error in this distribution.
What is the main limitation of the z test in behavioral research?
Explain why a t distribution is associated with n − 1 degrees of freedom and describe the information that is conveyed by the t statistic.
Making decisions in hypothesis testing. Toll, Kroesbergen, and Van Luit (2016) tested their hypothesis regarding real math difficulties among children. In their study, the authors concluded:“Our hypothesis [regarding math difficulties] was confirmed” (p. 429). In this example, what decision did
Sample size and power. Davis and Loprinzi (2016) evaluated a hypothesis related to engaging children, adolescents, and adults in physical activity. As part of their study, they reported a sample size of 106 children, 128 adolescents, and 440 adults. Assuming equal effect sizes across these age
Describing the z test. In an article describing hypothesis testing with small sample sizes, Collins and Morris (2008) provided the following description for a z test: “Z is considered significant if the difference is more than roughly two standard deviations above or below zero (or more
The value of a p value. In a critical commentary on the use of significance testing, Charles Lambdin (2012) explained, “If a p < .05 result is ‘significant,’ then a p = .067 result is not‘marginally significant’” (p. 76). Explain what the author is referring to in terms of the two
The one-tailed tests. In their book, Common Errors in Statistics (and How to Avoid Them), Good and Hardin (2003) wrote, “No one will know whether your [one-tailed] hypothesis was conceived before you started or only after you had examined the data” (p. 347). Why do the authors state this as a
Directional versus nondirectional hypothesis testing. Cho and Abe (2013) provided a commentary on the appropriate use of one-tailed and two-tailed tests in behavioral research. In their discussion, they outlined the following hypothetical null and alternative hypotheses to test a research
Will increasing sample size (n) increase or decrease the value of standard error? Will this increase or decrease power?
As α increases, so does the power to detect an effect. Why, then, do we restrict α from being larger than .05?
State whether the effect size for a 1-point effect (M − μ = 1) is small, medium, or large given the following population variances:1. σ = 1 2. σ = 2 3. σ = 4 4. σ = 6
Will each of the following increase, decrease, or have no effect on the value of Cohen’s d?1. The population variance is increased.2. The sample size is decreased.3. The sample variance is reduced.4. The difference between the sample and population mean is increased.
A local school reports that the average grade point average (GPA) in the entire school is a mean score of 2.66, with a standard deviation of 0.40. The school announces that it will be introducing a new program designed to improve GPA scores at the school. What is the effect size (d) for this
A national firm reports mean earnings of $75 ± $12 (μ ± σ) per unit sold over the lifetime of the company. A competing company over the past 36 reporting periods had reported mean earnings equal to $78 per unit sold. Conduct a one-sample z test to determine whether mean earnings (in dollars per
The physical fitness score for a population of police officers at a local police station is 72, with a standard deviation of 7 on a 100-point physical endurance scale. Suppose the police chief selects a sample of 49 local police officers from this population and records a mean physical fitness
Will each of the following increase, decrease, or have no effect on the value of a test statistic for the one-sample z test?1. The sample size is increased.2. The sample variance is doubled.3. The population variance is decreased.4. The difference between the sample mean and population mean is
For each obtained value stated below, (1) what is the decision for each if α = .05 (one-tailed test, upper-tail critical), and (2) what is the decision for each if α = .01 (two-tailed test)?1. zobt = 2.10 2. zobt = 1.70 3. zobt = 2.75 4. zobt = −3.30
For each p value stated below, (1) what is the decision for each if α = .05, and (2) what is the decision for each if α = .01?1. p = .1000 2. p = .0050 3. p = .0250 4. p = .0001
Determine the level of significance for a hypothesis test in each of the following populations given the specified standard error and critical values. Hint: Refer to the values given in Table 7.4:1. μ = 100, σM = 8, critical values: 84.32 and 115.68 2. μ = 100, σM = 6, critical value: 113.98 3.
A researcher conducts a one-sample z test and makes the decision to reject the null hypothesis.Another researcher selects a larger sample from the same population, obtains the same sample mean, and makes the decision to retain the null hypothesis using the same hypothesis test. Is this
A researcher selects a sample of 30 participants and makes the decision to retain the null hypothesis. She conducts the same study testing the same hypothesis with a sample of 300 participants and makes the decision to reject the null hypothesis. Give a likely explanation for why the two samples
The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 135 ± 20 pounds (μ ± σ). Suppose we select a sample of 100 children (n = 100) to test whether children in this population are gaining weight at a .05 level of significance.1. What is the
Explain why the following statement is true: The population standard deviation is always larger than the standard error when the sample size is greater than one (n > 1).
A researcher conducts a hypothesis test and concludes that his hypothesis is correct. Explain why this conclusion is never an appropriate decision in hypothesis testing.
Distinguish between the significance and the effect size of a result.
What three factors can be increased to increase power?
What three factors can be decreased to increase power?
Alpha (α) is used to measure the error for decisions concerning true null hypotheses. What is beta(β) error used to measure?
How are the rejection regions, the probability of a Type I error, the level of significance, and the alpha level related?
Is a one-tailed test associated with greater power than a two-tailed test? Explain.
What are the critical values for a one-sample nondirectional (two-tailed) z test at a .05 level of significance?
What is a Type I error (α)?
What is a Type II error (β)?
What is the power in hypothesis testing?
What are two decisions that a researcher makes in hypothesis testing?
State the four steps of hypothesis testing.
True or false: The effect size, power, and sample size of a study can affect the decisions we make in hypothesis testing.
When a population is associated with a small effect size, what can a researcher do to increase the power of the study?
As effect size decreases, what happens to the power?
As effect size increases, what happens to the power?
Which type of test, one-tailed or two-tailed, is susceptible to the possibility of committing a Type III error?
A researcher conducts a hypothesis test and finds that p = .0689. What is the decision for a hypothesis test at a .05 level of significance?
A researcher conducts a one-sample z test. The z statistic for the upper-tail critical test at a .05 level of significance is zobt = 1.84. What is the decision for this test?
Is the following set of hypotheses appropriate for a directional or a nondirectional hypothesis test?H0: μ = 35 H1: μ ≠ 35
The scores for a population are normally distributed with a mean equal to 25 and standard deviation equal to 6. A researcher selects a sample of 36 students and measures a sample mean equal to 23. For this example, 1. What is the value of Cohen’s d?2. Is this effect size small, medium, or large?
________ measures the size of an effect in a population, whereas ______________ measures whether an effect exists in a population.
State the two correct decisions that a researcher can make.
What type of error is associated with decisions to reject the null hypothesis?
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