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Statistics For The Behavioral Sciences 2nd Edition Susan A. Nolan, Thomas Heinzen - Solutions
IQ scores are designed to have a mean of 100 and a standard deviation of 15. IQ testing is one way in which people are categorized as having different levels of mental disabilities; there are four levels of mental retardation between the IQ scores of 0 and 70.a. People with IQ scores of 20–35 are
Hurricane Katrina hit New Orleans on August 29, 2005. The National Weather Service Forecast Office maintains online archives of climate data for all U.S.cities and areas. These archives allow us to find out, for example, how the rainfall in New Orleans that August compared to the other months of
For each of the following examples (the same as in Exercise 7.41), state the null hypothesis and the research hypothesis, in both words and symbolic notation:a. A researcher is interested in studying the use of antibacterial products and the dryness of people’s skin.He thinks these products might
For each of the following examples, identify whether the research has expressed a directional or nondirectional hypothesis:a. A researcher is interested in studying the use of antibacterial products and the dryness of people’s skin.He thinks these products might alter the moisture in skin
Another teacher decides to average the height of all male students in all of his classes throughout the day. By the end of the day, he has measured the heights of 57 boys and calculated an average of 68.1 inches (l 67 inches and r 3.19 inches).a. Calculate the mean and standard error of the
Using what we know about the height of 15-year-old girls (again, l 63.8 inches and r 2.66 inches), imagine that a teacher finds the average height of 14 female students in one of her classes to be 62.4 inches.a. Calculate the mean and standard error of the distribution of mean heights.b. Calculate
Imagine your statistics professor lost all records of students’ raw scores on a recent test. However, she did record students’ z scores for the test, as well as the class average of 41 out of 50 points and the standard deviation of 3 points (treat these as population parameters).She informs you
Imagine a basketball team comprised of thirteen 15-year-old boys. The average height of the team is 69.5 inches. Remember, l 67 inches and r 3.19 inches.
Imagine a class of thirty-three 15-year-old girls with an average height of 62.6 inches. Remember, l 63.8 inches and r 2.66 inches.a. Calculate the z statistic.b. How does this sample of girls compare to the distribution of sample means?c. What is the percentile rank for this sample?
Kona, a 15-year-old boy, is 72 inches tall. According to the CDC, the average height at this age is 67.00 inches with a standard deviation of 3.19 inches.a. Calculate Kona’s z score.b. What is Kona’s percentile score for height?c. What percentage of boys this age are shorter than Kona?d. What
Elena, a 15-year-old girl, is 58 inches tall. Based on what we know, the average height for girls at this age is 63.80 inches, with a standard deviation of 2.66 inches.a. Calculate her z score.b. What percentage of girls are taller than Elena?c. What percentage of girls are shorter?d. How much
For each of the following, indicate whether or not the situation describes misleading data that the researcher may decide to investigate and potentially discard.a. A sample of 50 students rate their agreement with 100 statements designed to assess their political attitudes. The rating scale goes
Assume that the following set of data represents the responses of 10 participants to three similar statements.The participants rated their agreement with each statement on a scale from 1 to 7.a. There is a piece of dirty data in this data set. Identify it and explain why it is dirty.b. Assume that
Use the cutoffs of 1.65 and a p level of approximately 0.10, or 10%. For each of the following values, determine if you would reject or fail to reject the null hypothesis:a. z 0.95b. z 1.77c. A z statistic that 2% of the scores fall above
If the cutoffs for a statistical test are 2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases:a. z 0.94b. z 2.12c. A z score for which 49.6% of the data fall between z and the mean
If the cutoffs for a statistical test are 1.96 and 1.96, determine whether you would reject or fail to reject the null hypothesis in each of the following cases:a. z 1.06b. z 2.06c. A z score beyond which 7% of the data fall in each tail
You are conducting a hypothesis test based on a sample of 132 people for whom you observed a mean SAT verbal score of 490. Using the information in Exercise 7.27, calculate the mean and spread of the comparison distribution (lM and rM).
If you are performing a hypothesis test using a z statistic in which you sampled 50 people and found an average SAT verbal score of 542 (assume we know the population mean to be 500 and the standard deviation to be 100), calculate the mean and spread of the comparison distribution (lM and rM).
Calculate the percentage of scores in a one-tailed critical region for each of the following p levels:a. 0.05b. 0.10c. 0.01
For each of the following p levels, what percentage of the data will be in each critical region for a two-tailed test?a. 0.05b. 0.10c. 0.01
If the critical values for a hypothesis test occur where 2.5% of the distribution is in each tail, what are the cutoffs for z?
Rewrite each of the following probabilities, or p levels, as percentages:a. 0.19b. 0.04c. 0.92
Rewrite each of the following percentages as probabilities, or p levels:a. 5%b. 83%c. 51%
Using the z table in Appendix B, calculate the following for a z score of 1.71:a. Above this z scoreb. Below this z scorec. At least as extreme as this z score
Using the z table in Appendix B, calculate the following percentages for a z score of 0.08:a. Above this z scoreb. Below this z scorec. At least as extreme as this z score
Calculate the following percentages for a z score of 0.74, with a tail of 22.96%:a. What percentage of scores falls below this z score?b. What percentage of scores falls between the mean and this z score?c. What proportion of scores falls below a z score of 0.74?
How can misleading data result in missing data?
What are three ways to deal with missing data?
What are three kinds of dirty data and what are their possible sources?
What is the difference between a one-tailed hypothesis test and a two-tailed hypothesis test in terms of critical regions?
Using everyday language, rather than statistical language, explain why the word cutoff might have been chosen to define the point beyond which we reject the null hypothesis.
Using everyday language, rather than statistical language, explain why the words critical region might have been chosen to define the area in which we reject the null hypothesis.
What do these symbolic expressions mean: H0: l1 l2 and H1: l1 l2?
What does statistically significant mean to statisticians?
What is the standard size of the critical region used by statisticians?
What are critical values and the critical region?
What are the six steps of hypothesis testing?
What is the difference between parametric tests and nonparametric tests?
What sample size is recommended in order to meet the assumption of a normal distribution, even when the population of interest is not normal?
In statistics, what do we mean by assumptions?
How is calculating a percentile for a mean from a distribution of means different from doing so for a score from a distribution of scores?
How do we calculate the percentage of scores below a particular positive z score?
When we look up a z score on the z table, what information can we report?
What is a percentile?
Credit card companies will often call cardholders if the pattern of use indicates that the card might have been stolen. Let’s say that you charge an average of $280 a month on your credit card, with a standard deviation of$75. The credit card company will call you anytime your purchases for the
The three most common treatments for blocked coronary arteries are medication, bypass surgery, or angioplasty, a medical procedure that involves clear ing out arteries and that leads to higher profits for doctors than do the other two procedures. The high est rate of angioplasty in the United
friends.a. What is the independent variable in this study? Is this variable nominal, ordinal, or scale?b. What is the dependent variable in this study? Is this variable nominal, ordinal, or scale?c. What is the null hypothesis for this study?d. What is the research hypothesis for this study?e.
through 6.45. Let’s say that you decide to use the GSS data to test whether peo -ple who live in rural areas have a different mean number of friends than does the overall GSS sample.Again, treat the overall GSS sample as the entire population of interest. Let’s say that you select 40 people
Refer to Exercise 6.43. Again, pretend that the GSS sample is the entire population of interest.a. Imagine that you randomly selected 80 people from this population who had a mean of 8.7.Would you compare this sample mean to a distribution of scores or a distribution of means? Explain your
Refer to Exercise 6.43. Again, pretend that the GSS sample is the entire population of interest.a. Imagine that you randomly selected one person from this population who reported that he had 18 close friends. Would you compare his score to a distribution of scores or a distribution of means?
and the mode is 4.00.a. Are these data for a distribution of scores or a distribution of means? Explain.b. What do the mean and standard deviation suggest about the shape of the distribution? (Hint: Compare the sizes of the mean and the standard deviation.)c. What do the three measures of central
The General Social Survey (GSS) is a survey of approximately 2000 adults conducted each year since 1972, for a total of more than 38,000 people. During several years of the GSS, participants were asked how many close friends they have. The mean for this variable is 7.44 friends, with a standard
You may need to find an apartment to rent upon graduation. The Internet is a valuable source of data to aid you in your search. From neighborhood safety to available transportation to housing costs, recent data can steer you in the right direction. On a Web site, San Mateo County in California
The revised version of the Minnesota Multiphasic Personality Inventory (MMPI-2) is the most frequently administered self-report personality measure. Test-takers respond to more than 500 true/false statements, and their responses are scored, typically by a computer, on a number of scales (e.g.,
is actually a projected number rather than a mean for a sample.)a. What is the variable of interest?b. What is the population?c. What is the sample?d. For the population, describe what the distribution of scores would be.e. For the population, describe what the distribution of means would be.f. If
years (Schackman et al., 2006).Imagine that the researchers determined this by following 250 people with HIV who were receiving ART and calculating the mean. (The
Researchers have reported that the projected life expectancy for people diagnosed with human immuno -deficiency virus (HIV) and receiving antiretroviral therapy (ART) is
Let’s look at baseball and football again. We’ll look at data for all of the teams in Major League Baseball(MLB) and the National Football League (NFL), respectively.a. In 2005, the mean number of wins for MLB teams was 81.00, with a standard deviation of 10.83.The perennial underdogs, the
Our statistics students, as noted in Exercise 6.32, were asked to rate their admiration of Hillary Rodham Clinton on a scale of 1 to 7. They also were asked to rate their admiration of Jennifer Lopez and Venus Williams on a scale of 1 to 7. As noted earlier, the mean rating of Clinton was 4.06,
A common quandary faces sports fans who live in the same city but avidly follow different sports. How does one determine whose team did better with respect to its league division? In 2004, the Boston Red Sox won the World Series; just months later, their local football counterparts, the New England
times per week, with a standard deviation of 2.4. For this exercise, imagine that this is the entire population of interest; thus, these numbers can be treated as parameters.a. Roughly, what is the percentile for a student who eats breakfast four times per week?b. Roughly, what is the percentile
Georgiou and colleagues (1997) reported that college students had healthier eating habits, on average, than did those who were neither college students nor college graduates. The 412 students in the study ate breakfast a mean of
For each of the following variables, state whether the distribution of scores would likely approximate a normal curve. Explain your answer.a. Number of movies that a college student watches in a yearb. Number of full-page advertisements in a magazinec. Human birth weights in Canada
A CFC study found a mean CFC score of 3.51, with a standard deviation of 0.61, for the 664 students in the sample (Petrocelli, 2003).a. Imagine that your z score on the CFC score is 1.2. What is your raw score? Use symbolic notation and the formula. Explain why this answer makes sense.b. Imagine
We have already discussed summary parameters for CFC scores for the population of participants in a study by Petrocelli (2003). The mean CFC score was 3.51, with a standard deviation of 0.61. (Remember that even though this was a sample, we treated the sample of 664 participants as the entire
A sample of 148 of our statistics students rated their level of admiration for Hillary Rodham Clinton on a scale of 1 to 7. The mean rating was 4.06, and the standard deviation was 1.70. (For this exercise, treat this sample as the entire population of interest.)a. Use these data to demonstrate
A sample of 150 statistics students reported the typical number of hours that they sleep on a weeknight. The mean number of hours was 6.65, and the standard deviation was 1.24. (For this exercise, treat this sample as the entire population of interest.)a. What is always the mean of the z
The verbal subtest of the GRE has a population mean of 500 and a population standard deviation of 100 by design (the quantitative subtest has the same mean and standard deviation).a. Use symbolic notation to state the mean and standard deviation of the GRE verbal test.b. Convert a GRE score of 700
minutes. Here are the data for 40 of those students:30 90 60 60 5 90 30 40 45 60 60 30 90 60 25 10 90 20 15 60 60 75 45 60 30 75 15 30 45 1 20 25 45 60 90 10 105 90 30 60
We asked 150 students (in our statistics classes) how long, in minutes, they typically spent getting ready for a date. The scores range from 1 minute to 120 minutes, and the mean is
Compute z statistics for each of the following, assuming the population has a mean of 100 and a standard deviation of 20:a. A mean of 101 is observed based on a sample of 43 scores.b. A mean of 96 is observed based on a sample of 60 scores.c. A mean of 100 is observed based on a sample of 29
A parent population has a mean of 55 and a standard deviation of 8. Compute lM and rM for each of the following samples:a. N 30b. N 300c. N 3000
Compute the standard error (rM) for each of the following, assuming the population has a mean of 100 and standard deviation of 20:a. Samples of size 45b. Samples of size 100c. Samples of size 4500
Evaluate the distribution of scores, expressed in percentages, for each of the following, assuming a normal distribution:a. How many scores fall below the mean?b. How many scores fall between 1 standard deviation below the mean and 2 standard deviations above the mean?c. What percentage of scores
Compare the following scores:a. A score of 811 when l 800 and r 29 against a score of 4524 when l 3127 and r 951b. A score of 17 when l 30 and r 12 against a score of 67 when l 88 and r 16
Compare the following “apples and oranges”: a score of 45 when the population mean is 51 and the standard deviation is 4 and a score of 732 when the population mean is 765 and the standard deviation is 23.a. Convert these scores to standardized scores.b. Using the standardized scores, what can
A study of the Consideration of Future Consequences(CFC) scale found a mean score of 3.51, with a standard deviation of 0.61, for the 664 students in the sample(Petrocelli, 2003). For the sake of this exercise, let’s assume that this particular sample comprises the entire population of
Using what we know about the population of GRE scores from Exercise 6.20, convert the same z scores to raw scores using symbolic notation and the formula.a. 1.5b. –0.5c. –2.0
The verbal subtest of the Graduate Record Examination (GRE) has a population mean of 500 and a population standard deviation of 100 by design. Convert the following z scores to raw scores without using a formula.a. 1.5b. –0.5c. –2.0
Another population has a mean of 1179 and a standard deviation of 164. Return each of the following z scores to original scores.a. –0.23b. 1.41c. 2.06d. 0.03
For a population with a mean of 250 and a standard deviation of 47, return each of the following z scores to original scores on this variable.a. 0.54b. –2.66c. –1.0d. 1.79
Using the population described in Exercise 6.14, compute the z score for 203 and 297. Explain the significance of these values.
Using the population described in Exercise 6.14, compute the z score for 250. Explain the meaning of the value you obtain.
A population has a mean of 1179 and a standard deviation of 164. Calculate z scores for each of the following observations:a. 1000b. 721c. 1531d. 1184
If a population has a mean of 250 and standard deviation of 47, calculate z scores for each of the following observations:a. 391b. 273c. 199d. 160
Create a histogram for these three sets of scores. Each set of scores represents a sample taken from the same population?
Each of the following equations has an error. Identify and fix the error and explain your work.
What does a z statistic—a z score based on a distribution of means—tell us about a sample mean?
Why does the standard error become smaller simply by increasing the sample size?
What does the symbol lM stand for?
Why is the central limit theorem such an important idea for dealing with a population that is not normally distributed?
What are the mean and standard deviation of the z distribution?
Give three reasons why z scores are useful.
What is a z score?
Explain how the word standardize is used in everyday conversation; then explain how statisticians use it.
How does the size of a sample of scores affect the distribution of data?
What point on the normal curve represents the most commonly occurring observation?
Explain how the word normal is used in everyday conversation; then explain how statisticians use it.
Borsari and Carey (2005) randomly assigned 64 male students who had been ordered, after a violation of university alcohol rules, to meet with a school counselor to one of two conditions. Students were assigned to undergo either (1) a brief motivational interview (BMI), a recently developed
Imagine you have made a new acquaintance in your statistics class with whom you study for tests. One day after hours of studying, your study partner asks you to go on a date. This invitation takes you by complete surprise and you have no idea what to say. You are not attracted to the person in a
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