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statistics for experimentert
Statistics For The Behavioral Sciences 10th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions
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 following:a. Increasing the difference between the sample mean and the original population mean.b.
If the alpha level is changed from α = .05 to α = .01,a. What happens to the boundaries for the critical region?b. What happens to the probability of a Type I error?
How does an increase in the value of σ influence the likelihood of rejecting the null hypothesis and the power of the hypothesis test?a. The likelihood of rejecting H0 and the power of the test both increase.b. The likelihood of rejecting H0 and the power of the test both decrease.c. The
How does increasing the sample size influence the likelihood of rejecting the null hypothesis and the power of the hypothesis test?a. The likelihood of rejecting H0 and the power of the test both increase.b. The likelihood of rejecting H0 and the power of the test both decrease.c. The likelihood of
Which of the following defines the power of a hypothesis test?a. The probability of rejecting a true null hypothesisb. The probability of supporting true null hypothesisc. The probability of rejecting a false null hypothesisd. The probability of supporting a false null hypothesis
Identify the factors that influence power and explain how power is affected by each.
Define the power of a hypothesis test and explain how power is related to the probability of a Type II error.
If other factors are held constant, then how does the size of the standard deviation affect the likelihood of rejecting the null hypothesis and the value for Cohen’s d?a. A larger standard deviation increases the likelihood of rejecting the null hypothesis and increases the value of Cohen’s
A treatment is administered to a sample selected from a population with a mean ofµ = 80 and a standard deviation of σ = 10.After treatment, the sample mean is M = 85.Based on this information, the effect size as measured by Cohen’s d is _____.a. d = 5.00b. d = 2.00c. d = 0.50d. impossible to
Which of the following is most likely to reject the null hypothesis even if the treatment effect is very small?a. A small sample and a small value for σ.b. A small sample and a large value for σ.c. A large sample and a small value for σ.d. A large sample and a large value for σ.
Explain how measures of effect size such as Cohen’s d are influenced by the sample size and the standard deviation.
Explain why it is necessary to report a measure of effect size in addition to the outcome of a hypothesis test.
A researcher expects a treatment to produce an increase in the population mean.The treatment is evaluated using a one-tailed hypothesis test, and the test produces z = –1.85. Based on this result, what is the correct statistical decision?a. The researcher should reject the null hypothesis with α
A sample is selected from a population with a mean of µ = 45 and a treatment is administered to the sample. If the treatment is expected to produce a decrease in the scores, then what would be the null hypothesis for a directional hypothesis test?a. µ ≥ 45b. µ ≤ 45c. M ≤ 45d. M ≥ 45
A researcher is predicting that a treatment will increase scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test ______.a. would be entirely in the right-hand tail of the distributionb. would be entirely in the left-hand tail of the
A sample of n = 16 individuals is selected from a population with µ = 80 and σ = 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 standard deviation to σ = 25?a. Increase the chances that the sample
Which of the following is not an assumption for the z-score hypothesis test?a. The observations must be independent.b. The value for μ must be the same after treatment as it was before treatment.c. The value for σ must be the same after treatment as it was before treatment.d. The sample must be
A research report summarizes the results of the hypothesis test by stating, “z = 2.13, p < .05.” Which of the following is a correct interpretation of this report?a. The null hypothesis was rejected and the probability of a Type I error is less than .05.b. The null hypothesis was rejected and
Explain how the outcome of a hypothesis test is influenced by the sample size, standard deviation, and difference between the sample mean and the hypothesized population mean.
Explain how the results of a hypothesis test with a z-score test statistic are reported in the literature.
What is a likely outcome for a hypothesis test if a treatment has a very small effect?a. a Type I errorb. a Type II errorc. correctly reject the null hypothesisd. correctly fail to reject the null hypothesis
Which of the following defines a Type II 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
When does a researcher risk a Type I error?a. anytime H0 is rejectedb. anytime H1 is rejectedc. anytime the decision is “fail to reject H0”d. All of the other options are correct.
A researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 1.77. Assuming that the researcher is using a two-tailed test,a. The researcher should reject the null hypothesis
What is the correct decision in a hypothesis if the data produce a z-score that is in the critical region?a. Reject H0b. Fail to reject H0c. Reject H1d. Fail to reject H1
A researcher selects a sample of n = 20 from a normal population with μ = 80 andσ = 20, and a treatment is administered to the sample. If a hypothesis test is used to evaluate the effect of the treatment, what is the null hypothesis?a. μ = 80b. M = 80c. μ • 80d. M • 80
A sample of n = 16 individuals is selected from a population with μ = 40 andσ = 12, and a treatment is administered to the sample. After treatment, the sample mean is M = 42.How does this sample compare to samples that should be obtained if the treatment has no effect?a. It is an extreme value
Conduct a hypothesis test and make a statistical decision about the effect of a treatment.
Define the alpha level (level of significance) and the critical region for a hypothesis test.
Define the null hypothesis and the alternative hypothesis for a hypothesis test.
A normal distribution has a mean of μ = 65 and a standard deviation of σ = 20.For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of its size.a. M = 74 for a sample of
A random sample is obtained from a normal population with a mean of μ = 95 and a standard deviation of σ = 40.The sample mean is M = 86.a. Is this a representative sample mean or an extreme value for a sample of n = 16 scores?b. Is this a representative sample mean or an extreme value for a
A normal distribution has a mean of μ = 60 and a standard deviation of σ = 18.For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size.a. M = 67 for n = 4
Callahan (2009) conducted a study to evaluate the effectiveness of physical exercise programs for individuals with chronic arthritis. Participants with doctor-diagnosed arthritis either received a Tai Chi course immediately or were placed in a control group to begin the course 8 weeks later. At the
Jumbo shrimp are those that require 10–15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages μ = 12.5 with a standard deviation of σ = 1, and forms a normal distribution. What is the probability of randomly picking a sample of n = 25 1-pound bags that
The distribution ages for students at the state college is positively skewed with a mean of μ = 21.5 and a standard deviation of σ = 3.a. What is the probability of selecting a random sample of n = 4 students with an average age greater than 23? (Careful: This is a trick question.)b. What is the
For random samples of size n = 25 selected from a normal distribution with a mean of mean of μ = 50 and a standard deviation of σ = 20, find each of the following:a. The range of sample means that defines the middle 95% of the distribution of sample means.b. The range of sample means that defines
A population has a mean of μ = 30 and a standard deviation of σ = 8a. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 4?b. If the population distribution is positively skewed, what is the probability of obtaining
A normal distribution has a mean of μ = 54 and a standard deviation of σ = 6.a. What is the probability of randomly selecting a score less than X = 51?b. What is the probability of selecting a sample of n = 4 scores with a mean less than M = 51?c. What is the probability of selecting a sample of
IQ scores form a normal distribution with a mean ofμ = 100 and a standard deviation of σ = 15.What is the probability of obtaining a sample mean greater than M = 103,a. for a random sample of n = 9 people?b. for a random sample of n = 25 people?c. for a random sample of n = 100 people?
Scores on a standardized reading test for 4th-grade students form a normal distribution with μ = 60 andσ = 20.What is the probability of obtaining a sample mean greater than M = 65 for each of the following:a. a sample of n = 16 studentsb. a sample of n = 25 studentsc. a sample of n = 100 students
A population forms a normal distribution with a mean of μ = 55 and a standard deviation of σ = 12.For each of the following samples, compute the z-score for the sample mean.a. M = 58 for n = 4 scoresb. M = 58 for n = 16 scoresc. M = 58 for n = 36 scores
A sample of n = 25 scores has a mean of M = 68.Find the z-score for this sample:a. If it was obtained from a population with μ = 60 and σ = 10.b. If it was obtained from a population with μ = 60 and σ = 20.c. If it was obtained from a population with μ = 60 and σ = 40.
For a population with a mean of μ = 40 and a standard deviation of σ = 8, find the z-score corresponding to each of the following samples.a. X = 36 for a sample of n = 1 scoreb. M = 36 for a sample of n = 4 scoresc. M = 36 for a sample of n = 16 scores
For a sample of n = 16 scores, what is the value of the population standard deviation (σ) necessary to produce each of the following a standard error values?a. σM = 8 points?b. σM = 4 points?c. σM = 1 point?
If the population standard deviation is σ = 10, how large a sample is necessary to have a standard error that isa. less than 5 points?b. less than 2 points?c. less than 1 point?
For a population with σ = 12, how large a sample is necessary to have a standard error that is:a. less than 4 points?b. less than 3 points?c. less than 2 points?
For a population with a mean of μ = 45 and a standard deviation of σ = 10, what is the standard error of the distribution of sample means for each of the following sample sizes?a. n = 4 scoresb. n = 25 scores
A population has a standard deviation of σ = 24.a. On average, how much difference should there be between the sample mean and the population mean for a random sample of n = 4 scores from this population?b. On average, how much difference should there be for a sample of n = 9 scores?c. On average,
The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not be normal?
Describe the distribution of sample means (shape, mean, standard error) for samples of n = 64 selected from a population with a mean of μ = 90 and a standard deviation of σ = 32.
A sample is selected from a population with a mean ofμ = 40 and a standard deviation of σ = 8.a. If the sample has n = 4 scores, what is the expected value of M and the standard error of M?b. If the sample has n = 16 scores, what is the expected value of M and the standard error of M?
If a sample of n = 25 scores is selected from a normal population with µ = 80 andσ = 10, then what sample means form the boundaries that separate the middle 95%of all sample means from the extreme 5% in the tails?a. 76.08 and 83.92b. 76.70 and 83.30c. 77.44 and 82.56d. 78 and 82
A random sample is obtained from a population with µ = 80 and σ = 10 and a treatment is administered to the sample. Which of the following outcomes would be considered noticeably different from a typical sample that did not receive the treatment?a. n = 25 with M = 81b. n = 25 with M = 83c. n =
If a sample is selected from a normal population with µ = 50 and σ = 20, which of the following samples is extreme and very unlikely to be obtained?a. M = 45 for a sample of n = 4 scores.b. M = 45 for a sample of n = 25 scores.c. M = 45 for a sample of n = 100 scores.d. The three samples are
Explain how the distribution of sample means can be used to evaluate a treatment effect by identifying likely and very unlikely samples.
For a particular population, the standard distance between a sample mean and the population mean is 5 points for samples of n = 4 scores. What would the standard distance be for samples of n = 16 scores?a. 5 pointsb. 4 pointsc. 2.5 pointsd. 1 point
For samples selected from a population with µ = 40 and σ = 20, what sample size is necessary to make the standard distance between the sample mean and the population mean equal to 2 points?a. n = 2b. n = 10c. n = 25d. n = 100
For samples selected from a population with µ = 100 and σ = 15, which of the following has the smallest standard error?a. a sample of n = 4 scoresb. a sample of n = 16 scoresc. a sample of n = 25 scoresd. The three samples all have the same standard error.
Describe how the magnitude of the standard error is related to the size of the sample.
A random sample of n = 25 scores is selected from a normally distributed population with μ = 500 and σ = 100.What is the probability that the sample mean will be less than 490?a. 0.4602b. 0.3085c. 0.1587d. 0.0062
A random sample of n = 9 scores is obtained from a population with µ = 50 and σ = 9.If the sample mean is M = 53, what is the z-score corresponding to the sample mean?a. z = 0.33b. z = 1.00c. z = 3.00d. cannot determine without additional information
A normal population has µ = 50 and σ = 8.A random sample of n = 16 scores from this population has a mean of 54.What is the z-score for this sample mean?a. +0.50b. +1.00c. +2.00d. +4.00
Describe the circumstances in which the distribution of sample means is normal and, in these circumstances, find the probability associated with a specific sample.
The standard distance between a sample mean and the population mean is 6 points for samples of n = 16 scores selected from a population with a mean of μ = 50.What is the standard deviation for the population?a. 48b. 24c. 6d. 3
If random samples, each with n = 4 scores are selected from a population withµ = 80 and σ = 12, then how much distance is expected on average between the sample means and the population mean?a. 4(12) = 48 pointsb. 12 pointsc. 12 4 = 3 pointsd. 12Ï4 = 6 points
If samples are selected from a population with μ = 80 and σ = 12, then which of the following samples will have the largest expected value for M?a. n = 10 scores with M = 82b. n = 20 scores with M = 84c. n = 30 scores with M = 86d. All of the samples will have the same expected value.
Describe how the standard error of M is calculated, explain what it measures, and describe how it is related to the standard deviation for the population.
Explain how the central limit theorem specifies the shape, central tendency, and variability for the distribution of sample means.
If all the possible random samples of size n = 25 are selected from a population with μ = 80 and σ = 10 and the mean is computed for each sample, then what shape is expected for the distribution of sample means?a. The sample means tend to form a normal-shaped distribution whether the population
All the possible random samples of size n = 2 are selected from a population withμ = 40 and σ = 10 and the mean is computed for each sample. Then all the possible samples of size n = 25 are selected from the same population and the mean is computed for each sample. How will the distribution of
If all the possible random samples of size n = 5 are selected from a population withμ = 50 and σ = 10 and the mean is computed for each sample, then what value will be obtained for the mean of all the sample means?a. 50b. 50 5 = 10c. 50(5) = 2500d. Around 50 but probably not equal to 50.
Define the distribution of sample means and describe the logically predictable characteristics of the distribution.
The student health clinic reports that only 30% of students got a flu shot this year. If a researcher surveys a sample of n = 84 students attending a basketball game,a. What is the probability that any individual student has had a flu shot?b. What is the probability that more than 30 students have
A test developed to measure ESP involves using Zener cards. Each card shows one of five equally likely symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person
A roulette wheel has alternating red and black, numbered slots into which the ball finally stops to determine the winner. If a gambler always bets on black to win, thena. What is the probability of winning at least 40 times in a series of 64 spins? (Note that at least 40 wins means 40 or more.)b.
A true/false test has 20 questions. If a student is simply guessing at the answers,a. On average, how many questions would a student answer correctly for the entire test?b. What is the probability that a student would answer more than 15 questions correctly simply by guessing?c. What is the
A multiple-choice test has 32 questions, each with four response choices. If a student is simply guessing at the answers,a. What is the probability of guessing correctly for any individual question?b. On average, how many questions would a student answer correctly for the entire test?c. What is the
Rochester, New York, averages μ = 21.9 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard deviation of σ = 6.5 inches. A local jewelry store advertised a refund of 50% off all purchases made in December, if we have more than 3
A report in 2010 indicates that Americans between the ages of 8 and 18 spend an average of μ = 7.5 hours per day using some sort of electronic device such as smart phones, computers, or tablets. Assume that the distribution of times is normal with a standard deviation of σ = 2.5 hours and find
According to a recent report, people smile an average of μ = 62 time per day. Assuming that the distribution of smiles is approximately normal with a standard deviation of σ = 18, find each of the following values.a. What proportion of people smile more than 80 times a day?b. What proportion of
The distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100.For the population of students who have taken the SAT,a. What proportion have SAT scores less than 400?b. What proportion have SAT scores greater than 650?c. What is the
IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ =15. Find the proportion of the population in each of the following IQ categories.a. Genius or near genius: IQ over 140b. Very superior intelligence: IQ from 120–140c. Average
In 2014, the New York Yankees had a team batting average of μ = 245 (actually 0.245 but we will avoid the decimals). Of course, the batting average varies from game to game, but assuming that the distribution of batting averages for 162 games is normal with a standard deviation is σ = 40 points,
A normal distribution has a mean of μ = 30 and a standard deviation of σ = 12.For each of the following scores, indicate whether the body is to the right or left of the score and find the proportion of the distribution located in the body.a. X = 33b. X = 18c. X = 24d. X = 39
A normal distribution has a mean of μ = 70 and a standard deviation of σ = 8.For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the tail.a. X = 72b. X = 76c. X = 66d. X = 60
Find each of the following probabilities for a normal distribution.a. p(–0.80 < z < 0.80)b. p(–0.50 < z < 1.00)c. p(0.20 < z < 1.50)d. p(–1.20 < z < –0.80)
Find each of the following probabilities for a normal distribution.a. p(z > 1.25)b. p(z > –0.60)c. p(z < 0.70)d. p(z < –1.30)
Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body.a. z = 2.50b. z = 0.80c. z = –0.50d. z = –0.77
Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the tail is on the right or left side of the line and find the proportion in the tail.a. z = 1.00b. z = 0.50c. z = –1.25d. z = –0.40
A psychology class consists of 28 males and 52 females.If the professor selects names from the class list using random sampling,a. What is the probability that the first student selected will be a female?b. If a random sample of n = 3 students is selected and the first two are both females, what is
Around Halloween each year the grocery store sells three-pound bags of candy contains a mixture of three different mini-bars: Snickers, Milky Way, and Twix.If the bag has an equal number of each of the three bars, then what are the probabilities for each of the following?a. Randomly selecting a
An individual is selected from a normal population with μ = 100 and σ = 10 and a treatment is administered to the individual. After treatment, the individual has a score of X = 125.What is the probability that individual with a score this high or higher would be obtained if the treatment has no
For a normal distribution with μ = 100 and σ = 10, what X values separate the middle 95% from the extreme values in the tails of the distribution?a. X = 83.5 and X = 116.5b. X = 80.4 and X = 119.6c. X = 87.2 and X = 112.8d. X = 95 and X = 105
For a normal distribution with μ = 100 and σ = 10, which of the following accurately describes the location of X = 80?a. It is an extreme, very unlikely score.b. It is a low score, but not extreme or unlikely.c. It is a fairly representative score.d. None of the other options is an accurate
If you are simply guessing on a true/false test with 36 questions, what is the probability that you will get 20 or more correct?a. 0.1587b. 0.2033c. 0.2514d. 0.3085
For a binomial distribution with p = 1 4, what is the probability that A will occur more than 18 times in a series of 48 trials?a. 0.2514b. 0.0336c. 0.0228d. 0.0150
What is the standard deviation for a binomial distribution with p = q = 1 2 and n = 36?a. 3b. 9c. 12d. 18
Calculate the probability associated with a specific X value in a binomial distribution and find the score associated with a specific proportion of a binomial distribution.
Describe the circumstances in which the normal distribution serves as a good approximation to the binomial distribution.
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