PSY-380 Week 2 Homework State the statistical notation for each of the following terms

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1. State the statistical notation for each of the following terms.

(a) population size

• • n
  • N
  • M or X
  • μ

(b) sample size

• • M or X
  • n
  • μ
  • N

(c) population mean

• • μ
  • M or X
  • n
  • N

(d) sample mean

• • N
  • n
  • μ
  • M or X

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2. The mean is an appropriate measure for describing what types of data?

• The mean is an appropriate measure for data that are normally distributed on an interval or ratio scale of measurement.
• The mean is an appropriate measure for data that are skewed on an ordinal scale of measurement.
• The mean is an appropriate measure for data that are normally distributed on an ordinal scale of measurement.
• The mean is an appropriate measure for data that are skewed on an interval or ratio scale of measurement.

3. The mode is an appropriate measure for describing what types of data?

• The mode is used without other measures of central tendency for normally distributed interval data.
• The mode is used with other measures of central tendency for any nonmodal distribution.
• The mode is used with other measures of central tendency for any modal distribution and for nominal data.
• The mode is used without other measures of central tendency for normally distributed ratio data.

4. The following frequency distribution table lists the time (in minutes) that participants were late for an experimental session. Compute the sample mean, median, and mode for these data.

mean

median

mode

Time (min)	Frequency
0	3
3	5
6	2
7	1
9	2

5. A researcher records the number of hours (per week) that single mothers spend at work and states that the data are distributed normally. Which measure of central tendency is most appropriate for describing these data?

• the median
• the mode
• the mean

6. A researcher records the levels of attraction for various fashion models among college students. He finds that mean levels of attraction are much higher than the median and mode for these data.

(a) What is the shape of the distribution for the data described in this study?

• • normal distribution
  • positively skewed distribution
  • negatively skewed distribution
  • bimodal distribution

(b) Which measure of central tendency is most appropriate for describing these data? Explain.

The _median_______ is best because the data are __positively skewed_____

7. A neuroscientist measures the reaction times (in seconds) during an experimental session in a sample of cocaine-addicted (n = 6), morphine-addicted (n = 12), and heroin-addicted rats (n = 8). Mean reaction times in each sample were 17, 13, and 12 seconds, respectively. What is the weighted mean for all three samples? Hint: The overall mean is not 14.0 seconds. (Round your answer to two decimal places.)
8. Based on the scale of measurement for each variable listed below, which measure of central tendency is most appropriate for describing the data?

(a) the distance in miles that a group of athletes run to train for a marathon

• • the median
  • the mean
  • the mode

(b) the rankings of college undergraduate academic programs

• • the median
  • the mean
  • the mode

(c) the blood type (e.g., Type A, B, AB, O) of a group of participants

• • the median
  • the mean
  • the mode

9. A group of researchers measure the weight of five participants prior to a clinical weight loss intervention. They record the following weights (in pounds): 150, 250, 300, 200, and 100 pounds. The mean is 200 pounds.

Using the original example of five weights, the researchers added a sixth participant to the sample.

(a) If the sixth participant weighed 210 pounds, will the mean increase, decrease, or not change?

• • The mean will increase.
  • The mean will decrease.
  • The mean will not change.

(b) If the sixth participant weighed 200 pounds, will the mean increase, decrease, or not change?

• • The mean will increase.
  • The mean will decrease.
  • The mean will not change.

(c) If the sixth participant weighted 170 pounds, will the mean increase, decrease, or not change?

• • The mean will increase.
  • The mean will decrease.
  • The mean will not change.

10. Gilman and colleagues (2008) measured general life satisfaction in 1,338 adolescents from two individualistic nations (Ireland, United States) and two collectivist nations (China, South Korea) using the Multidimensional Students’ Life Satisfaction Scale (MSLSS). Mean participant scores on the MSLSS are given in the following table.

Nation	Gender
	Men	Women
United States	4.39	4.61
Ireland	4.37	4.64
China	4.41	4.56
South Korea	3.92	3.78

(a) Among which group was general life satisfaction lowest on average?

• • men from China
  • women from the United States
  • men from Ireland
  • women from South Korea
  • men from the United States
  • women from Ireland
  • men from South Korea
  • women from China

(b) Among which group was general life satisfaction highest on average?

• • men from the United States
  • women from Ireland
  • women from the United States
  • men from China
  • women from South Korea
  • men from Ireland
  • men from South Korea
  • women from China

11. What are the degrees of freedom for sample variance?

• n
• n − 1
• n − 2
• n + 1

12. Based on the empirical rule, what percentage of data fall within 1 SD, 2 SD, and 3 SD of the mean for data that are distributed normally? (Enter your answers to one decimal place.)

• __________ % of all scores lie within 1 SD of the mean
• __________ % of all scores lie within 2 SD of the mean
• __________ % of all scores lie within 3 SD of the mean

13. A social scientist measures the number of minutes (per day) that a small hypothetical population of college students spends online.

Student	Score	Student	Score
A	94	F	85
B	79	G	65
C	31	H	95
D	87	I	96
E	94	J	87

(a) What is the range of data in this population? ___ min

(b) What is the IQR of data in this population? ___ min

(c) What is the SIQR of data in this population? ___ min

(d) What is the population variance? ___ min

(e) What is the population standard deviation? (Round your answer to two decimal places.)  ___ min

14. A sociologist records the annual household income (in thousands of dollars) among a sample of families living in a high-crime neighborhood. Locate the lower, median, and upper quartiles for the times listed below. Hint: First arrange the data in numerical order.

lower quartile             _____         thousand dollars

median             _____         thousand dollars

upper quartile             _____         thousand dollars

39	37
46	49
27	22
39	43
54	31

15. A forensic psychologist records the number of criminal offenses among teenage drug users in a nationwide sample of 1,501 participants. To measure the variance of criminal offenses, he computes SS = 13,500 for this sample.

(a) What are the degrees of freedom for variance?

(b) Compute the variance and standard deviation.

variance                     ___________

standard deviation              ___________

16. State whether each of the following will increase, decrease, or have no effect on the population variance.

(a) the sum of squares (SS) increases

• • This change will increase the population variance.
  • This change will decrease the population variance.
  • This change will have no effect on the population variance.

(b) the sample size decreases

• • This change will increase the population variance.
  • This change will decrease the population variance.
  • This change will have no effect on the population variance.

(c) the size of the population increases

• • This change will increase the population variance.
  • This change will decrease the population variance.
  • This change will have no effect on the population variance.

17. A researcher measures the time (in seconds) it takes a sample of five participants to complete a memory task. It took four of the participants 4, 5, 5, and 6 seconds. If M = 6, then what must be the fifth time recorded?

18. An expert reviews a sample of 10 scientific articles (n = 10) and records the following number of errors in each article: 4, 8, 6, 0, 5, 7, 2, 9, 6, and 6. Compute SS, variance, and standard deviation for this sample using the definitional and computational formula. (Round your answers to two decimal places.)

SS		errors
Variance		errors
Standard deviation		errors

19. A professor records the time (in minutes) that it takes 16 students to complete an exam. Compute the SS, the variance, and the standard deviation assuming the 16 students constitute a population and assuming the 16 students constitute a sample. (Round your answers for variance and standard deviation to two decimal places.)

22	47	50	34
16	27	31	25
42	41	46	40
45	31	35	56

(a) the 16 students constitute a population

SS		min
Variance		min
Standard deviation		min

(b) the 16 students constitute a sample

SS		min
Variance		min
Standard deviation		min

1. 20. To study bonding between mothers and infants, a researcher places each mother and her infant in a playroom and has the mother leave for 10 minutes. The researcher records crying time in the sample of infants during this time that the mother was not present and finds that crying time is normally distributed with M = 4 and SD = 1.3. Based on the empirical rule, state the range of crying times within 68% of infants cried, 95% of infants cried, and 99.7% of infants cried.

(a) 68% of infants cried ___ to ____ min

 (b) 95% of infants cried ___ to ____ min

 (c) 99.7% of infants cried ___ to ____ min

1. 21. Salska and colleagues (2008) studied height preferences among dating partners. In their first study, they reviewed Yahoo personals for heterosexual individuals living within 250 miles of Los Angeles, California, and recorded the acceptable range of heights for their dating partners. The following table lists some of the results. Overall, did men or women show greater variability in their responses? Explain.

	Women		Men
Preferences	M	SD	M	SD
Shortest acceptable height, inches	68.9	2.6	60.6	3.7
Tallest acceptable height, inches	75.3	2.2	69.8	2.7

• • Women showed greater variability overall because the standard deviations for women were smaller than for men.
  • Men showed greater variability overall because the standard deviations for men were larger than for women.
  • Men showed greater variability overall because the means for men were smaller than for women.
  • Women showed greater variability overall because the means for women were larger than for men.

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Course: PSY-380 Introduction to Probability and Statistics
School: Grand Canyon University

• Due Date (Double Check): 08/12/2019
• Willing to Pay (USD): 100