# 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 cfants cried

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.

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Time (min)  Frequency
0     3
5     2
6     5
7     1
9     2
______________________________________________________________________________
7. A neuroscientist measures the reaction times (in seconds) during an experimental session in a sample of cocaine-addicted
(n = 8),
(n = 6),
(n = 12).
Mean reaction times in each sample were 16, 14, 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.)
____________ sec
______________________________________________________________________________
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): 160, 110, 210, 310, and 260 pounds. The mean is 210 pounds.
Using the original example of five weights, the researchers added a sixth participant to the sample.
(a) If the sixth participant weighed 220 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 210 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 180 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?
women from South Korea
men from the United States
women from Ireland
men from South Korea
women from the United States
men from China men from Ireland
women from China
(b) Among which group was general life satisfaction highest on average?
women from South Korea
men from Ireland
men from South Korea
men from the United States
women from China
women from Ireland
women from the United States
men from China
______________________________________________________________________________
11. What are the degrees of freedom for sample variance?
n − 2
n + 1
n − 1
n
______________________________________________________________________________
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   64   F    84
B   86   G   97
C   27   H  92
D   91   I   78
E   92   J    86
(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?
(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
22  36
46  53
38  49
47  31
20  38
______________________________________________________________________________
15. A psychopathologist records the number of criminal offenses among teenage drug users in a nationwide sample of 1,301 participants. To measure the variance of criminal offenses, he computes SS = 46,800 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 1, 2, 2, and 3 seconds. If M = 2, then what must be the fifth time recorded?
______________sec
______________________________________________________________________________
18, An expert reviews a sample of 10 scientific articles (n = 10) and records the following number of errors in each article: 3, 5, 4, 6, 9, 0, 1, 9, 0, and 8. Compute SS, variance, and standard deviation for this sample using the definitional and computational formula. (Round your answers to two decimal places.)
SS   ________________________
variance ________________________
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.)
31  39  42  28
43  51  41  20
36  22  19  42
13  40  24  49
(a) the 16 students constitute a population
SS ______________________
variance ____________________
standard deviation ___________________min
(b) the 16 students constitute a sample
SS ___________________
variance _____________________
standard deviation ___________________min
______________________________________________________________________________
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 = 8 and SD = 1.1.
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 cfants cried
______________ to _____________ min
(b) 95% of infants cried
___________ried.
(a) 68% of in___ to ______________ min
(c) 99.7% of infants cried
______________ to ______________ min

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