Statistics For The Behavioral Sciences 4th Edition Gregory J Privitera - Solutions

Explore the comprehensive solutions for "Statistics For The Behavioral Sciences 4th Edition" by Gregory J Privitera, now available online. Access the answers key and solutions PDF, offering step-by-step answers to every question. Whether you're looking for solved problems, test bank insights, or chapter solutions, our solution manual has got you covered. Ideal for students and instructors alike, this resource provides an instructor manual and textbook solutions to enhance understanding. Enjoy the convenience of free download options, making it easier than ever to grasp complex statistical concepts with detailed questions and answers.

Given that ¯X = 78, σ2 = 25, n = 10, and α = 0.05, test H0: μ > 80, assuming observations are randomly sampled from a normal distribution.Also, draw the standard normal distribution indicating where Z and the critical value are located.
Using R, set the R variable val=0. Next, generate 25 values from a binomial distribution where the possible number of successes is 0–6 and the probability of success is 0.9. This can be accomplished with the command rbinom(20,6, 0.9). The resulting observations will have values between 0 and 6
An ABC news program reported that a standard method for rendering patients unconscious resulted in patients waking up during surgery.These individuals were not only aware of their plight, they suffered from nightmares later. Some physicians tried monitoring brain function during surgery to avoid
For 16 presidential elections in the United States, the incumbent party won or lost the election depending on whether the American football team, the Washington Redskins, won their last game just prior to the election. Verify that according to Blythe’s method, a 0.99 confidence for the
If the mean and trimmed mean are nearly identical, it might be thought that it makes little difference which measure of location is used. Based on your answer to the previous problem, why might it make a difference?
In the previous problem, the length of the confidence interval for μ is 257.6 − 200.7 = 56.9 and the length based on the trimmed mean is 244.9 − 196.7 = 48.2. Comment on why the length of the confidence interval for the trimmed mean is shorter.
Chapter 2 reported data on the number of seeds in 29 pumpkins. The results were 250, 220, 281, 247, 230, 209, 240, 160, 370, 274, 210, 204, 243, 251, 190, 200, 130, 150, 177, 475, 221, 350, 224, 163, 272, 236, 200, 171, 98.The 20% trimmed mean is ¯Xt = 220.8 and the mean is ¯X = 229.2.Verify that
Under normality, the sample mean has a smaller standard error than the trimmed mean or median. If observations are sampled from a distribution that appears to be normal, does this suggest that the mean should be preferred over the trimmed mean and median?
In a portion of a study of self-awareness, Dana (1990) observed the values 59, 106, 174, 207, 219, 237, 313, 365, 458, 497, 515, 529, 557, 615, 625, 645, 973, 1065, 3215.Compare the lengths of the confidence intervals based on the mean and 20% trimmed mean. Why is the latter confidence interval
Compare the length of the confidence interval in the previous problem to length of the length of the confidence interval for the mean you obtained in Exercise 31. Comment on why they differ.
Compute a 0.95 confidence interval for the 20% trimmed mean using the data in Table 4.3.
Repeat the previous exercise, but compute a 0.99 confidence interval instead.
Compute a 0.95 confidence interval for the 20% trimmed mean if (a)n = 24, s2 w = 12, ¯Xt = 52, (b) n = 36, s2 w = 30, ¯Xt = 10, (c) n = 12, s2 w = 9, ¯Xt = 16.
When sampling from a light-tailed, skewed distribution, where outliers are rare, a small sample size is needed to get good probability coverage, via the central limit theorem, when the variance is known. How does this contrast with the situation where the variance is not known and confidence
Rats are subjected to a drug that might affect aggression. Suppose that for a random sample of rats, measures of aggression are found to be 5, 12, 23, 24, 18, 9, 18, 11, 36, 15.Compute a .95 confidence for the mean assuming the scores are from a normal distribution.
Table 4.3 reports data from a study on self-awareness. Compute a 0.95 confidence interval for the mean.
Repeat the previous exercise, but compute a 0.99 confidence interval instead.
Compute a 0.95 confidence interval if (a) n = 10, ¯X = 26, s = 9, (b)n = 18, ¯X = 132, s = 20, (c) n = 25, ¯X = 52, s = 12.
Describe a type of continuous distribution where the central limit theorem gives good results with small sample sizes.
Describe a situation where Equation (4.11), used in conjunction with the central limit theorem, might yield a relatively long confidence interval.
You sample 16 observations from a discrete distribution with mean μ =36 and variance σ2 = 25. Use the central limit theorem to determine(a) P( ¯X < 34), (b) P( ¯X < 37), (c) P( ¯X > 33), (d) P(34 < ¯X < 37).
A company claims that the premiums paid by its clients for auto insurance has a normal distribution with mean μ = $750 dollars and standard deviation σ = 100. Assuming normality, what is the probability that for n = 9 randomly sampled clients, the sample mean will a value between$700 and $800?
Explain why knowing the mean and squared standard error is not enough to determine the distribution of the sample mean. Relate your answer to results on non-normality described in Chapter 3.
Chapter 3 described a mixed normal distribution that differs only slightly from a standard normal. Suppose we randomly sample n = 25 observations from a standard normal distribution. Then the squared standard error of the sample mean is 1/25. What is the squared standard error if sampling is from
In Exercise 16, if the observations are dependent, can you still estimate the standard error of the sample mean?
For the values 6, 3, 34, 21, 34, 65, 23, 54, 23, estimate the squared standard error of the sample mean.
In Exercise 14, verify that there are outliers. What are the effects of these outliers on the estimated squared standard error?
As part of a health study, a researcher wants to know the average daily intake of vitamin E for the typical adult. Suppose that for n = 12 adults, the intake is found to be 450, 12, 52, 80, 600, 93, 43, 59, 1000, 102, 98, 43.Estimate the squared standard error of the sample mean.
If you randomly sample a single observation and get 32, what is the estimate of the population mean, μ? Can you get an estimate of the squared standard error? Explain, in terms of the squared standard error, why only a single observation is likely to be a less accurate estimate ofμ versus a
Suppose you randomly sample n = 8 participants and get 2, 6, 10, 1, 15, 22, 11, 29.Estimate the variance and standard error of the sample mean.
Answer the same question posed in the previous problem, only replace means with sample variances.
In the previous problem, again suppose you sample n = 12 participants and compute the sample mean. If you repeat this process 1000 times, each time using n = 12 participants, and if you averaged the resulting 1000 sample means, approximately what would be the result? That is, approximate the
Suppose you randomly sample n = 12 observations from a discrete distribution with the following probability function:x: 1 2 3 4 p(x): .2 .1 .5 .2 Determine E( ¯X ) and σ2¯X.
If n = 10 observations are randomly sampled from a distribution with mean μ = 9 and variance σ2 = 8, what is the mean and variance of the sample mean?
Describe the two components of a random sample.
For the following situations, (a) n = 12, σ = 22, ¯X = 65, (b) n = 22,σ = 10, ¯X = 185, (c) n = 50, σ = 30, ¯X = 19, compute a 0.95 confidence interval for the mean.
A manufacturer claims that its light bulbs have an average life span of μ = 1200 h with a standard deviation of σ = 25. If you randomly test 36 light bulbs and find that their average life span is ¯X = 1150, does a 0.95 confidence interval for μ suggest that the claim μ = 1200 is unreasonable?
Repeat the previous example, only compute a 0.99 confidence interval instead.
Assuming random sampling is from a normal distribution with standard deviation σ = 5, if you get a sample mean of ¯X = 45 based on n = 25 participants, what is the 0.95 confidence interval for μ?
If you want to compute a 0.80, 0.92, or a 0.98 confidence interval forμ when σ is known, and sampling is from a normal distribution, what values for c should you use in Equation (4.8)?
Explain the meaning of a 0.95 confidence interval.
In the previous problem, determine E(X), the variance of X, E(ˆp), and the variance of ˆp.
Determine P(μ − σ ≤ X ≤ μ + σ) for the probability function x: 1, 2, 3, 4 p(x): 0.2, 0.4, 0.3, 0.1
If a distribution is skewed, is it possible that the mean exceeds the 0.85 quantile?
If a distribution appears to be bell-shaped and symmetric about its mean, can we assume that the probability of being within one standard deviation of the mean is 0.68?
For normal random variables, the probability of being within one standard deviation of the mean is 0.68. That is, P(μ−σ ≤ X ≤ μ+σ) = .68 if X has a normal distribution. For non-normal distributions, is it safe to assume that this probability is again 0.68? Explain your answer.
Suppose the daily amount of solar radiation in Los Angeles is normally distribution with mean 450 calories and standard deviation 50. Determine the probability that for a randomly chosen day, the amount of solar radiation is between 350 and 550.
A large computer company claims that its salaries are normally distributed with mean $50,000 and standard deviation 10,000. What is the probability of observing an income between $40,000 and $60,000?
A manufacturer of car batteries claims that the life of its batteries is normally distributed with mean μ = 58 months and standard deviationσ = 3. Determine the probability that a randomly selected battery will last at least 62 months.
In the previous problem, how high must someone score to be in the top 5%? That is, determine c such that P(X >c) = 0.05.
If X has a normal distribution, determine c such that P(μ − cσ < X < μ + cσ) = 0.8.
If X has a normal distribution, determine c such that P(μ − cσ < X < μ + cσ) = 0.95.
If X has a normal distribution with mean μ = .75 and standard deviationσ = 0.5, determine (a) P(X < 0.25), (b) P(X > 0.9), (c) P(0.5 < X
If Z has a standard normal distribution, find c such that (a) P(Z >c) = 0.0764, (b) P(Z >c) = 0.5040, (c) P(−c ≤ Z
If Z has a standard normal distribution, find c such that (a) P(Z ≤c) = 0.0099, (b) P(Z c) = 0.5691, (d) P(−c ≤ Z ≤c) = 0.2358.
If Z has a standard normal distribution, determine (a) P(Z < −0.5),(b) P(Z < 1.2), (c) P(Z > 2.1), (d) P(−0.28 < Z < 0.28).
If Z has a standard normal distribution, determine (a) P(Z ≤ 0.5), (b)P(Z > −1.25), (c) P(−1.2 < Z < 1.2), (d) P(−1.8 ≤ Z < 1.8).
Given that Z has a standard normal distribution, use Table 1 in Appendix B to determine (a) P(Z ≥ 1.5), (b) P(Z ≤ −2.5), (c) P(Z
For the previous problem, determine the 0.8 quantile.
When you look at a clock, the number of minutes past the hour, say X, is some number between 0 and 60. Assume the number of minutes past the hour has a uniform distribution. Determine (a) P(X = 30),(b) P(X ≤ 10), (c) P(X ≥ 20), (d) P(10 ≤ X < 20).
Suppose the waiting time at a traffic light has a uniform distribution from 0 to 20 seconds. Determine (a) the probability of waiting exactly 12 seconds, (b) less than 5 seconds, (c) more than 10 seconds.
For the uniform distribution with a = −1 and b = 1, determine c such that (a) P(−c ≤ X ≤c) = .9, (b) P(−c ≤ X ≤c) = 0.95, (c) P(−c ≤ X ≤c) = 0.99
For the uniform distribution with a = −1 and b = 1, determine c such that (a) P(X ≤c) = 0.9, (b) P(X ≤c) = 0.95, (c) P(X >c) = 0.99.
For the uniform distribution in the previous problem, determine the median, the 0.25, and the 0.9 quantiles.
For the uniform distribution over the interval -3 to 2, determine (a)P(X ≤ 1), (b) P(X < −1.5), (c) P(X > 0), (d) P(−1.2 ≤ X ≤ 1.), (e)P(X = 1).
The probability density function associated with a so-called uniform dis-tribution is given by f(x) = 1/(b−a), where a and b are given constants and a ≤ x ≤b. That is, the possible values you might observe range between the constants a and b with every value between a and b equally likely. If
Coleman (1964) interviewed 3398 schoolboys and asked them about their self-perceived membership in the “leading crowd.” Their response was either yes, they were a member, or no they were not. The same boys were also asked about their attitude concerning the leading crowd. In particular, they
For the following probabilities Income Age High Medium Low< 30 0.030 0.180 0.090 30-50 0.052 0.312 0.156> 50 0.018 0.108 0.054 determine (a) the probability someone is under 30, (b) the probability that someone has a high income given that they are under 30, (c) the probability of someone having a
Verify that if we standardize the possible values in the previous exercise, the resulting mean is zero and the variance is one.
For the probability function x: 1, 2, 3, 4, 5 p(x): 0.2, 0.2, 0.2, 0.2, 0.2 would you expect the variance to be larger or smaller than the variance associated with the probability function used in the previous exercise?Verify your answer by computing the variance.
For the probability function x: 1, 2, 3, 4, 5 p(x): 0.1, 0.25, 0.3, 0.25, 0.1 would you expect the variance to be larger or smaller than the variance associated with the probability function used in the previous exercise?Verify your answer by computing the variance for the probability function
For the probability function x: 1, 2, 3, 4, 5 p(x): 0.15, 0.2, 0.3, 0.2, 0.15 determine the mean, the variance, and P(X ≤ μ).
Standardizing the possible values in the previous exercise means that we transform the possible values (0 and 1) by subtracting the population mean and dividing by the population standard deviation. Here this yields (1−0.3)/√0.21 = 0.7/√0.21 and (0−0.3)/√0.21 = −0.3/√0.21,
For the probability function x: 0, 1 p(x): 0.7, 0.3 verify that the mean and variance are 0.3 and 0.21. What is the probability of getting a value less than the mean?
In a study conducted by M. Earleywine, one goal was to measure hangover symptoms after consuming a specific amount of alcohol in a laboratory setting. The resulting measures, written in ascending order, were 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 3, 3, 3, 6,
Looking at Figure 2.2, what approximately is the interquartile range?How large or small must a value be to be declared an outlier?
For the data in Table 2.3, use R to verify that the value 3.05 is an outlier based on the boxplot rule.
Use the results of the last problem to come up with a general rule about how many outliers a boxplot can detect.
For the values 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 there are no outliers. If you increase 10 to 20, then 20 would be declared an outlier by a boxplot.(a) If the value 9 is also increased to 20, would the boxplot find two outliers? (b) If the value 8 is also increased to 20, would the boxplot find all
Snedecor and Cochran (1967) report results from an experiment on weight gain in rats as a function of source of protein and levels of protein.One of the groups was fed beef with a low amount of protein. The weight gains were 90, 76, 90, 64, 86, 51, 72, 90, 95, 78.Verify that there are no outliers
For a sample of n participants, the relative frequencies are f0/n = .2, f1/n = .4, f2/n = .2, f3/n = .15, and f4/n = .05. The sample mean is 1.45. Using your answer to Exercise 18, verify that the sample variance is 1.25.
One million couples are asked how many children they have. Suppose the relative frequencies are f0/n = .10, f1/n = .20, f2/n = .25, f3/n = .29, f4/n = .12, and f5/n = .04. Compute the sample variance.
Devise a method for computing the sample variance based on the frequencies, fx.
For the data used in Exercise 6, which values would be declared outliers using the rule based on MAD?
For the data in Exercise 14, determine the ideal fourths and the corresponding interquartile range.
For the data in Exercise 6, verify that the sample variance is 5584.9 and the Winsorized sample variance is 1375.6.
Repeat the previous problem but for s2 w instead. Assume 20% Winsorization.
Among a sample of 25 participants, what is the minimum number of participants that must be altered to make the sample variance arbitrarily large?
In the previous problem, what is the Winsorized variance if the value 49 is increased to 102?
For the observations 21, 36, 42, 24, 25, 36, 35, 49, 32 verify that the sample variance and the sample Winsorized variance are s2 = 81, s2 w = 51.4.
For the frequencies f1 = 12, f2 = 18, f3 = 15, f4 = 10, f5 = 8, and f6 = 5, verify that the sample mean is 3.
Suppose health inspectors rate sanitation conditions at restaurants on a five-point scale where a 1 indicates poor conditions and a 5 is excellent.Based on a sample of restaurants in a large city, the frequencies are found to be f1 = 5, f2 = 8, f3 = 20, f4 = 32, and f5 = 23. What is the sample
A class of fourth graders was asked to bring a pumpkin to school. Each of the 29 students counted the number of seeds in their pumpkin and the results were 250, 220, 281, 247, 230, 209, 240, 160, 370, 274, 210, 204, 243, 251, 190, 200, 130, 150, 177, 475, 221, 350, 224, 163, 272, 236, 200, 171,
For the observations 6, 3, 2, 7, 6, 5, 8, 9, 8, 11 verify that the sample mean, 20% trimmed mean, and median are ¯X =6.5, ¯X t = 6.7, and M = 6.5.
For the data in Exercise 1, what is the minimum number of observations that must be altered so that the 20% trimmed mean is greater than 1000?
The largest observation in the first problem is 49. If 49 is replaced by the value 200, verify that the sample mean is now ¯X = 50.1 but the trimmed mean, and median are not changed. What does this illustrate about the resistance of the sample mean?
For the observations 21, 36, 42, 24, 25, 36, 35, 49, 32 verify that the sample mean, 20% trimmed mean, and median are ¯X =33.33, ¯Xt = 32.9, and M = 35.
Using APA style, which of the following nonparametric tests can be reported either with the original test statistic or with the z score for the normal approximation of that test?a. the sign testb. the Mann-Whitney U testc. the Wilcoxon signed-ranks T testd. All of these.
Which of the following nonparametric tests requires that the degrees of freedom are reported using APA style?a. the sign testb. the Friedman testc. the Mann-Whitney U testd. the Wilcoxon signed-ranks T test
What is the decision for this Friedman test?a. Fail to reject the null hypothesis.b. Reject the null hypothesis.

Showing 3500 - 3600 of 8686

First
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Last

Statistics For The Behavioral Sciences 4th Edition Gregory J Privitera - Solutions

Step by Step Answers