Soc 274, Section 02: Social Statistics



Soc 274, Section 02: Social Statistics

Jeremiah Coldsmith

Summer 09, Final Exam

Name: ___________________________________

For each question show your work, so I can give you partial credit. Also make sure you answer all the parts of the question. For all calculations, label and circle your answers!

1) The following are the years of education completed for 15 employees at a local manufacturing plant.

10, 12, 12, 14, 12, 16, 16, 15, 14, 12, 13, 18, 20, 14, 12

a. Generate a Frequency Table, including frequency, cumulative frequency, percentage, and cumulative percentage.

b. Draw a histogram or bar chart to represent the frequency distribution of these employees’ years of education completed.

c. Calculate the Mode, Median, and Mean (If appropriate. If it is not appropriate, explain why it isn’t.)

d. Calculate the Range (If appropriate. If it is not appropriate, explain why it isn’t.)

e. Calculate the Deviations from the Mean and the Sum of the Squared Deviations. (Don’t forget to label and circle the answers. Make sure I know you know which numbers are which of these.)

|Workers |Years of Education Completed | | | |

|1 |10 | | | |

|2 |12 | | | |

|3 |12 | | | |

|4 |14 | | | |

|5 |12 | | | |

|6 |16 | | | |

|7 |16 | | | |

|8 |15 | | | |

|9 |14 | | | |

|10 |12 | | | |

|11 |13 | | | |

|12 |18 | | | |

|13 |20 | | | |

|14 |14 | | | |

|15 |12 | | | |

|Σ | | | | |

f. Calculate the Variance and the Standard Deviation.

2) What is the probability of each of the following?

a. Rolling a 3 on an 8 sided die.

b. Rolling a 3 on a 12 sided die.

c. Rolling an even number on a 6 sided die.

d. Rolling two 9s on two 10 sided dice at the same time.

e. Rolling an odd number on two consecutive rolls of an 8 sided die.

3) A test designed to evaluate reading comprehension ability is normally distributed with a mean of 10 and a standard deviation of 1.5. (Note: The scores are truly continuous. Round the scores to the nearest hundredths.)

a. what percent of test takers scored lower than someone who scored an 11.5?

b. what percent of test takers scored higher than someone who scored an 8?

c. what percent of test takers scored between the person who scored 11.5 and the one who scored 8?

d. what would someone need to score in order to have 25% of test takers score better than them?

e. what are the scores that bound the middle 95% of test takers?

4) A team of political sociologists are concerned that the racial makeup of their most recent sample of union members is not representative of the population of union members. They believe that the union member population is 75% white, 20% black, and 5% other. Their sample of 670 registered voters has 565 whites, 85 blacks, and 20 others. The pollsters want to be 99% sure the sample is different from their expectations.

Calculate the appropriate statistic and let the pollsters know if their sample matches their expectations or not.

HR:

H0:

Level of Significance:

Degrees of Freedom:

Critical Value:

Calculate the χ2: (Note: Label and Circle the χ2 value.)

|Race |Observed Frequency | | | | |

|White |565 | | | | |

|Black |85 | | | | |

|Other |20 | | | | |

|Total |670 | | | | |

What decision do you make about the Hypotheses?

What conclusion can you draw from that decision?

5) Clinical psychologists are working on a new anger management therapy. They believe this new therapy will decrease aggressive behaviors of those with anger problems. They begin by observing how often their subjects become angered when confronted with a frustrating situation. Then, they perform the new therapy on the subjects. Finally, they observe the subjects again in situations similar to those prior to the therapy to see how often the subjects become angered now. The psychologists want to be 99% sure that the therapy decreases the number of aggressive behaviors exhibited by their subjects. Do the appropriate statistical test and interpret the results.

|Subject |Number of |Number of Post-therapy | | | | |

| |Pre-therapy Aggressive Acts |Aggressive Acts | | | | |

|1 |8 |6 | | | | |

|2 |6 |5 | | | | |

|3 |3 |4 | | | | |

|4 |8 |5 | | | | |

|5 |9 |6 | | | | |

|6 |4 |2 | | | | |

|Σ | | | | | | |

s.d.:

Level of Significance:

d.f.:

Critical Value:

HR:

H0:

Work for the statistical test:

Decision concerning the hypotheses:

Conclusion based on the decision:

6) A student who has had a sociology statistics course is trying to decide which of two on-line merchants to buy a product from. The prices, shipping costs, and time to deliver are exactly the same. The final thing the student would like to check is how well the two merchants are rated by previous customers. He would like to be 95% sure there is a difference in the ratings of the two stores before deciding from which one to buy. Do the appropriate statistical test and tell the student if the two stores are rated differently.

|Sample 1: First Store |

|Previous Customers |Rating out of 10 | | | |

|5 |8.8 | | | |

|4 |6.4 | | | |

|3 |8.7 | | | |

|2 |7.8 | | | |

|1 |8.3 | | | |

|Σ | | | | |

v1:

|Sample 2: Second Store |

|Previous Customers |Rating out of 10 | | | |

|4 |8.6 | | | |

|3 |8.9 | | | |

|2 |9.3 | | | |

|1 |9.2 | | | |

|Σ | | | | |

v2:

HR:

H0:

d.f.1:

d.f.2:

d.f.T:

Level of Significance:

Critical Value:

m1:

m2:

v1:

v2:

vpooled:

vm1:

vm2:

vdifference:

sdifference:

Work for the Statistical Test:

Decision concerning the hypotheses:

Conclusion based on the decision:

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