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fundamentals of statistics
Questions and Answers of
Fundamentals Of Statistics
What are the main characteristics of the Student t-distribution?
In what ways is the Student t-distribution similar to the standard normal distribution?
Why is there a different distribution of t-statistics for different sample sizes?
What happens to the shape of the t-distribution as the sample size grows larger?
What is the generic definition of degrees of freedom (df)?
Under what situations are degrees of freedom (df) calculated?
Why is there a table of critical values for the t-statistic rather than a single critical value?
What information is needed to identify the critical value for the t-statistic?
Under what situations would you conduct the z-test for one mean or the t-test for one mean?
What are the differences between the formulas for the population standard error of the mean and the standard error of the mean?
What are the similarities and differences between the formulas for the z-test and the t-test?
For each of the following situations, calculate the degrees of freedom and identify the critical values (assumeα = .05 [two-tailed]).a. N = 9b. N = 13c. N = 18d. N = 21
For each of the following situations, calculate the standard error of the mean (sX̅).a. s = 3.00; N = 16b. s = 7.50; N = 25c. s = 20.00; N = 50d. s = 3.41; N = 38
For each of the following situations, calculate the t-statistic (t). a. X=14.00; b. X 3.00; c. X.56; 9; s = 12.00; N = 36 5; s = 6.00; N = 16 .65; s = .18; N = 17
For each of the following situations, calculate the degrees of freedom (df), identify the critical values (assumeα = .05 [two-tailed]), calculate the t-statistic (t), make a decision about the null
For each of the following situations, calculate the degrees of freedom (df), identify the critical values (assumeα = .05 [two-tailed]), calculate the standard error of the mean (sX̅), calculate the
Identify the mode for each of the following sets of data:a. 7, 3, 7, 1, 7b. 3, 1, 1, 2, 3, 3c. 8, 22, 8, 10, 9, 8, 12, 7, 8d. 5, 3, 6, 4, 5, 3, 1, 5, 2, 5, 6, 5e. 11, 9, 13, 6, 14, 12, 7, 12, 10, 8,
Identify the mode for each of the following sets of data:a. 6, 2, 7, 6, 6, 4b. 13, 19, 12, 13, 7, 13, 20, 13, 15c. 4, 2, 5, 1, 2, 2, 5, 5, 3, 1, 5, 2, 6, 3d. 40, 10, 35, 30, 10, 25, 5, 10, 15, 10, 5,
Calculate the median for each of the following sets of data:a. 3, 4, 6, 7, 10b. 14, 16, 19, 21, 22, 27, 36c. 6, 6, 9, 9, 9, 10, 13, 16, 16, 21, 24d. 4, 2, 6, 3, 8, 3, 8e. 27, 24, 35, 30, 41, 32, 36,
Calculate the median for each of the following sets of data:a. 2, 2, 3, 4, 6, 9, 9b. 7, 7, 8, 12, 13, 14, 17, 21, 23c. 11, 6, 3, 14, 12, 15, 8, 10, 7d. 9, 6, 7, 5, 8, 7, 8, 9, 10, 8, 7e. 10, 13, 13,
Calculate the mean for each of the following sets of data:a. 2, 2, 3, 5b. 3, 5, 5, 7, 7, 8, 8, 11c. 9, 6, 7, 5, 8, 7, 8, 9, 10, 8, 7d. 11, 13, 14, 15, 16, 16, 16, 17, 18, 20, 22, 25e. 2.57, 3.62,
Calculate the mean for each of the following sets of data:a. 1, 1, 2, 3, 3b. 1, 4, 4, 5, 6, 7, 8c. 47, 56, 62, 69, 70, 73d. .75, .23, .48, .60, .98, .65, .08, .12, .39e. 11.02, 13.67, 17.39, 14.74,
Identify the mode in each of the following frequency distribution tables. a. b. Score f % st 4 5 31% 3 3 19% 2 6 38% 1 2 12% Total 16 100% Score f % 5 st 4 16% 4 8 32% 3 6 24% 2 3 12% 1 2 8% 0 2 8%
Using Formula 3-4, calculate the mean for the variables in the frequency distribution tables in Exercise 7.
If a variable with N = 25 has a mean of 3.25, what is the value of ΣX?
For the sets of data in Exercise 5(a) and (b), calculate the difference between each score and the mean (use Table 3.2 as an example). Next, compare the sum of the positive and negative differences
What makes you happy? Participants in a research experiment reported their levels of happiness and the amount of time spent alone versus with friends or family. The researchers found that people who
A friend of yours asks 20 people to rate a movie using a 1- to 5-star rating: the higher the number of stars, the higher the recommendation. Their ratings are listed below:a. Calculate the number of
One study stated the research hypothesis, “Violence behavior in children may be reduced by teaching them conflict resolution skills” (DuRant et al., 1996). The variable “violence behavior”
The 10% myth study discussed in this chapter measured the beliefs of both psychology majors and non–psychology majors. The 39 non–psychology majors in this study provided the following values for
At an ice skating competition, the score for each skater is the mean of the different judges’ scores. However, before this mean is calculated, the lowest and the highest scores among the judges are
Given the following values for the mode, median, and mean, determine whether you believe the distribution is symmetrical, positively skewed, or negatively skewed.a. Mode = 4, median = 5, mean = 8b.
On your own, generate a set of data where the mean, median, and mode are the same, and then create a figure for these data. How would you describe the shape of this distribution?
On your own, generate a set of data that is positively skewed, and then create a figure for these data. If you calculate the mean and median of these data, which is larger?
Why is it important to calculate measures of variability for a variable in addition to measures of central tendency?
What are the relative advantages and disadvantages of the range as a measure of variability?
What is the difference between the range and the interquartile range?
For what types of distributions might you report the interquartile range?
Calculate the range for each of the following sets of data:a. 2, 1, 4, 2, 7, 3b. 15, 6, 17, 9, 12, 5, 16, 7c. 21, 14, 13, 17, 30, 17, 14, 11, 13, 14, 19d. 3.0, 2.8, 3.2, 3.6, 3.7, 3.2, 3.5, 3.6, 3.1,
Calculate the interquartile range for each of the following sets of data:a. 9, 3, 2, 7, 15, 10, 14, 8b. 15, 6, 17, 9, 12, 5, 16, 7c. 13, 9, 9, 16, 10, 9, 5, 7, 9, 8, 10, 9d. 3.0, 2.8, 3.2, 3.6, 3.7,
Why does calculating the variance involve squaring the deviation of each score from the mean?
What is the purpose of computational formulas?
In calculating a measure of variability, why can’t you use the absolute value of the deviation of each score from the mean rather than the squared deviation?
In calculating the variance, why is the sum of squared deviations divided by N − 1 rather than N?
What is the difference between a biased estimate and an unbiased estimate?
Calculate the variance (s2) using the definitional and computational formulas for each of the following data sets.a. 2, 3, 3, 5, 7b. 5, 4, 7, 5, 10, 5, 6c. 10, 13, 13, 14, 15, 16, 17, 24d. 73, 66,
Is it possible to get a negative value for the variance or standard deviation? Why or why not?
Calculate the standard deviation (s) using the definitional and computational formula for each of the following data sets.a. 5, 3, 9, 2, 6b. 11, 19, 8, 10, 9, 7, 13c. 7, 9, 11, 12, 13, 14, 17, 21,
What is the main difference between the population standard deviation and the standard deviation?
Under what conditions would you calculate the population standard deviation for a set of data rather than the standard deviation?
Calculate the population standard deviation (σ) using the definitional and computational formula for each of the following data sets:a. 2, 4, 5, 6, 8b. 8, 6, 4, 8, 3, 7c. 71, 84, 65, 78, 89, 72, 60,
What is the main purpose of a measure of central tendency?
How do you identify the mode from a frequency distribution table or figure?
Determine the mode for each of the following sets of data.a. 2, 1, 4, 2, 7, 2, 3b. 6, 7, 6, 4, 5, 4, 2, 6c. 12, 5, 9, 12, 10, 11, 12, 8, 15, 12, 7d. 4, 2, 2, 1, 5, 4, 5, 2, 3, 2, 4, 2e. 3.0, 2.8,
a. Why are there different formulas for calculating the median depending on whether there are an odd or even number of scores for a variable?
Calculate the median for each of the following sets of data.a. 2, 3, 3, 4, 5, 6, 8b. 21, 14, 13, 17, 30, 17, 14, 11, 13, 14, 19c. 5, 6, 7, 9, 12, 15, 16, 17d. 73, 66, 91, 84, 69, 87, 62, 79, 82, 90e.
Why do we say that the mean is the balancing point in a distribution of scores?
Calculate the mean using Formula 3-3 for each of the following sets of data.a. 2, 3, 3, 5, 7b. 8, 6, 4, 8, 3, 7c. 71, 84, 65, 78, 89, 72, 60, 85d. 2.5, 1.0, 3.5, 3.0, 2.0, 2.5, 4.0, 1.0, 2.0e. 10, 8,
Calculate the mean using Formula 3-4 for the data in each of the following frequency distribution tables. a. LO 5 4 3 Score f do % 1 10% 1 10% 24 20% 40% 2 1 2 20% Total 10 100%
For the sets of data in 2(a) and 2(b), calculate the difference between each score and the mean (use Table 3.2 as an example). Next, compare the sum of the positive and negative differences to see if
What is the difference between the sample mean and the population mean (μ)?b. What is the difference between statistics and parameters?
What are the relative strengths and weaknesses of the mode, median, and mean as measures of central tendency? For what types of situations might you use one rather than another?
For which of the three aspects of distributions (modality, symmetry, and variability) do measures of central tendency provide information?
What are the main steps involved in the research process?
Why is it useful to review and evaluate theories and research before conducting a study?
What are the two main characteristics of research hypotheses?
What is the difference between an independent variable and a dependent variable?
What are the main differences between experimental and nonexperimental research methods?
What are confounding variables? What do researchers do to minimize the effects of confounding variables?
What are the main types of nonexperimental research methods?
What are the relative strengths and weaknesses of experimental and nonexperimental research?
What are the main purposes of descriptive and inferential statistics?
What is the difference between a population and a sample?
Within the research process, what is the relationship between populations and samples?
What are the four levels of measurement? How do they differ?
For each of the following variables, name the scale of measurement (nominal, ordinal, interval, or ratio).a. Type of school attended (public, private)b. Probability of graduating college in 4 years
What are some reasons for examining data before conducting statistical analyses?
Why are outliers of concern to researchers?
What questions do you address about a set of data for a variable in constructing frequency distribution tables?
Why is it useful to calculate percentages in addition to frequencies for each value of a variable?
For each of the following situations, create a frequency distribution table.a. A college counselor asks a group of 116 seniors what their plans are after graduating from college; 71 say they are
For what levels of measurement would you create a pie chart, bar chart, histogram, or a frequency polygon?
What is the difference between a bar chart and a histogram?
Why would it be inappropriate to create a histogram or frequency polygon for a nominal or ordinal variable?
Under what circumstances might you use a frequency polygon rather than a histogram to graph an interval or ratio variable?
For each of the following variables, identify whether you could use a bar chart, pie chart, histogram, and/or a frequency polygon to visually display the data.a. Miles per gallon (MPG)b. Living
What are the three aspects used to describe distributions of variables?
What is the difference between unimodal, bimodal, and multimodal distributions?
What is the difference between symmetric and asymmetric (skewed) distributions?
What is the difference between positively and negatively skewed distributions?
What is the difference between peaked and flat distributions?
What are the characteristics of a normally distributed variable?
For each of the following sets of data, determine whether the distribution of scores is unimodal, bimodal, or multimodal.a. 4, 2, 11, 6, 10, 2, 6, 13, 2, 10, 6, 10, 1b. 15, 17, 13, 18, 17, 14, 20,
For each of the following sets of data, determine whether the distribution of scores is symmetric or asymmetric (skewed).a. 4, 5, 1, 4, 2, 4, 3, 5, 3, 4, 4, 3b. 220, 230, 250, 230, 200, 240, 210,
For each of the following sets of data, determine whether the distribution of scores is peaked or flat.a. 16, 10, 19, 12, 13, 15, 14, 17, 15, 20, 11, 13, 19, 16, 15b. 12, 15, 12, 11, 13, 11, 12, 12,
You stop 10 people and ask them whether they would or would not recommend the movie to others. They give you the following answers:a. Construct a frequency distribution table of these data (be sure
One of your friends feels the responses of your 10 people did not result in a clear recommendation or nonrecommendation of the movie. She decides to ask 15 people to give the movie one of three
Your other friend asks 20 people to rate the movie using a 1- to 5-star rating: the higher the number of stars, the higher the recommendation. Their ratings are listed below:a. Construct a frequency
Another friend asks 30 people to rate the movie by their likelihood of seeing the movie again, ranging from 0% to 100%. Their ratings are listed below:a. Construct a grouped frequency distribution
Imagine you are in your local department store to buy a sweater. Which of the following signs would make you think you’re getting a good deal: “Everyday Low Price \($15.00\)” or “Regularly
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